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Recent questions tagged random-variable
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91
Probability- Gravner- 82.a
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (a) Compute the expectation $EM$.
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large.(a) Compute the expectation $EM$.
Pooja Khatri
497
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Pooja Khatri
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Sep 27, 2018
Probability
gravner
probability
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1
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92
Probability- Gravner- 81.b
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (b) Approximately how many times do you need to play so that you win at least $250$ dollar with probability at least $0.99$.
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads.(b) Approximately how many times do you need to play so that you win at least...
Pooja Khatri
331
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Pooja Khatri
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Sep 27, 2018
Probability
probability
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93
Probability- Gravner- 81.a
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads. (a) Assume that you play this game $300$ times. What is, approximately, the probability that you win at least $250$ dollar ?
Toss a fair coin twice. You win $1$ dollar if at least one of the two tosses comes out heads.(a) Assume that you play this game $300$ times. What is, approximately, the p...
Pooja Khatri
271
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Pooja Khatri
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Sep 27, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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1
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1
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94
Probability- Gravner- 80.c
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (c) ... $M$ be the amount of time of the show that you miss because of th call. Compute the expected value of $M$.
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that th...
Pooja Khatri
680
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Pooja Khatri
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Sep 27, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
uniform-distribution
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0
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1
answer
95
Probability- Gravner- 80.b
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval (b) At $8.30$, the call still hasn't arrived. What is the probability that it arrives in the next $10$ minutes?
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that th...
Pooja Khatri
434
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Pooja Khatri
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Sep 27, 2018
Probability
probability
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engineering-mathematics
random-variable
uniform-distribution
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0
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1
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96
Probability- Gravner- 80
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that the time $T$ of the call is uniformly distributed in the specified interval. (a) Compute the probability that the call arrives between $8.30$ and $8.20$.
After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that th...
Pooja Khatri
592
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Pooja Khatri
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Sep 27, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
uniform-distribution
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1
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97
Probability- Gravner- 79.c
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (c) Determine the probability density function of $Y$ $=$ $X^2$
A random variable $X$ has the density function$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$(c) Determine the probability density ...
Pooja Khatri
516
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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0
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98
Probability- Gravner- 79.b
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (b) Compute $\text{E(1/X)}$.
A random variable $X$ has the density function$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$(b) Compute $\text{E(1/X)}$.
Pooja Khatri
285
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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1
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99
Probability- Gravner- 79.a
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (a) Determine c.
A random variable $X$ has the density function$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$(a) Determine c.
Pooja Khatri
325
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Pooja Khatri
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Sep 26, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
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100
Probability- Gravner- 78
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
Pooja Khatri
316
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Pooja Khatri
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Sep 26, 2018
Probability
probability
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engineering-mathematics
random-variable
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101
Probability- Gravner- 77
A roulette wheel has $38$ slots: $18$ red, $18$ red, $2$ green. The ball ends at one of these at random. You are a player who plays a large number of games and makes an even bet of $1$ dollar on red in every game. After $n$ games, what is the probability that you are ahead? Answer this for $n=100$ and $n= 1000$.
A roulette wheel has $38$ slots: $18$ red, $18$ red, $2$ green. The ball ends at one of these at random. You are a player who plays a large number of games and makes an ...
Pooja Khatri
251
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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102
Probability- Gravner- 76
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.
Pooja Khatri
1.3k
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
normal-distribution
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0
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103
Probability- Gravner- 75.c
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
Pooja Khatri
292
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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1
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104
Probability- Gravner- 75.b
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
Pooja Khatri
239
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Pooja Khatri
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Sep 26, 2018
Probability
probability
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engineering-mathematics
random-variable
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2
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105
Probability- Gravner- 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
Pooja Khatri
649
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Pooja Khatri
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Sep 26, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
normal-distribution
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4
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2
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106
Probability - Gravner-74
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ > $0$. How is $Y$ distributed?
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ $0$. How is $Y$ distributed?
Pooja Khatri
765
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
normal-distribution
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0
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1
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107
Probability - Gravner-73
Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, compute the probability that it lasts more than $200$ hours and the probability that it lasts less than $50$ hours.
Assume that a light bulb lasts on average $100$ hours. Assuming exponential distribution, compute the probability that it lasts more than $200$ hours and the probability ...
Pooja Khatri
429
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Pooja Khatri
asked
Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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108
Probability - Gravner-72
A uniform random number $X$ divides $[0,1]$ into two segments. Let $R$ be the ratio of the smaller versus the larger segment. Compute the density of $R$.
A uniform random number $X$ divides $[0,1]$ into two segments. Let $R$ be the ratio of the smaller versus the larger segment. Compute the density of $R$.
Pooja Khatri
223
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Pooja Khatri
asked
Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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109
Probability - Gravner-71
Assume that X is uniform on [0,1]. What is $P(X\epsilon Q)$? What is the probability that the binary expansion of X starts with 0.010?
Assume that X is uniform on [0,1]. What is $P(X\epsilon Q)$? What is the probability that the binary expansion of X starts with 0.010?
Pooja Khatri
173
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Pooja Khatri
asked
Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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110
Probability - Gravner-70
Assume that X has density $fx(x) = \begin{Bmatrix} 3x^{2} &if(x\epsilon [0,1]), \\ 0& otherwise \end{Bmatrix}$ Compute the density fy of Y= 1-X4
Assume that X has density$fx(x) = \begin{Bmatrix} 3x^{2} &if(x\epsilon [0,1]), \\ 0& otherwise \end{Bmatrix}$Compute the density fy of Y= 1-X4
Pooja Khatri
240
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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1
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111
Probability - Gravner-69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$(c) Determine EX and Var(X).
Pooja Khatri
338
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Pooja Khatri
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Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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1
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112
Probability - Gravner-69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$(b) Compute $P(1\leqslant X\leqslant 2)$
Pooja Khatri
321
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Pooja Khatri
asked
Sep 26, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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0
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1
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113
Probability - Gravner-69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$(a) Determine $c$.
Pooja Khatri
246
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Pooja Khatri
asked
Sep 26, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
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0
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114
Probability - Gravner-68.d
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student' ... of the randomly chosen group. Let EY= $\mu$ and Var(Y) = $\sigma$2 . Express EX with s, n, $\mu$ and $\sigma$.
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...
Pooja Khatri
203
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Pooja Khatri
asked
Sep 25, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
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0
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0
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115
Probability - Gravner-68.c
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's group . Next, choose one the four groups at random and let $Y$ be its size. (c) Compute Var(X) and Var(Y).
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...
Pooja Khatri
289
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Pooja Khatri
asked
Sep 25, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
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0
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0
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116
Probability - Gravner-68.b
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of that student's group . Next, choose one the four groups at random and let $Y$ be its size. (b) Compute EX and EY.
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...
Pooja Khatri
162
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Pooja Khatri
asked
Sep 25, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
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0
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0
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117
Probability - Gravner-68.a
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. First choose one of the $50$ students at random and let $X$ be the size of ... , choose one the four groups at random and let $Y$ be its size. (a) Write down the probability mass functions for $X$ and $Y$.
Each of $50$ students in class belongs to exactly one the four groups $A,B,C$ or $D$. The membership numbers for the four groups are as follows: $A:5,B:5,C:15,D:20$. Firs...
Pooja Khatri
171
views
Pooja Khatri
asked
Sep 25, 2018
Probability
gravner
probability
engineering-mathematics
random-variable
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0
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0
answers
118
Probability - Gravner-67.a
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number of times the two dice have to be rolled before the game is decided. (a)Determine the probability mass function of N.
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number ...
Pooja Khatri
342
views
Pooja Khatri
asked
Sep 25, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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0
votes
1
answer
119
Probability - Gravner-67.c
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number of times the two dice have to be rolled before the game is ... dollar for winning in the first round, 1 dollar for winning in any other round, and nothing otherwise.Compute your expected winnings .
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number ...
Pooja Khatri
395
views
Pooja Khatri
asked
Sep 25, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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0
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1
answer
120
Probability - Gravner-67.b
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number of times the two dice have to be rolled before the game is decided. (b) Compute Probability you win
You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let $N$ be the number ...
Pooja Khatri
496
views
Pooja Khatri
asked
Sep 25, 2018
Probability
probability
gravner
engineering-mathematics
random-variable
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