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Recent questions tagged gravner
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Gravner- probability
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
ajaysoni1924
asked
in
Probability
Oct 23, 2019
by
ajaysoni1924
428
views
gravner
probability
engineering-mathematics
0
votes
0
answers
2
Probability- Gravner- 82.c
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (c) How large should $n$ be so that the probability in(b) is larger than $0.99$?
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
288
views
probability
gravner
engineering-mathematics
random-variable
1
vote
1
answer
3
Probability- Gravner- 82.b
Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large. (b) Write down an approximation, in terms on $n$ and $\phi$, of the probability that $M$ differs from its expectation by less than $10$ %
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
401
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
4
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 $EM$.
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
334
views
gravner
probability
engineering-mathematics
random-variable
1
vote
0
answers
5
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 $0.99$.
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
178
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
6
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 ?
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
177
views
probability
gravner
engineering-mathematics
random-variable
1
vote
1
answer
7
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 $M$.
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
430
views
probability
gravner
engineering-mathematics
random-variable
uniform-distribution
0
votes
1
answer
8
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?
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
295
views
probability
gravner
engineering-mathematics
random-variable
uniform-distribution
0
votes
1
answer
9
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 $8.20$.
Pooja Khatri
asked
in
Probability
Sep 27, 2018
by
Pooja Khatri
349
views
probability
gravner
engineering-mathematics
random-variable
uniform-distribution
0
votes
1
answer
10
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 $Y$ $=$ $X^2$
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
265
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
11
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 $\text{E(1/X)}$.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
161
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
12
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.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
188
views
gravner
probability
engineering-mathematics
random-variable
0
votes
1
answer
13
Probability- Gravner- 78
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
153
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
14
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 $n= 1000$.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
189
views
probability
gravner
engineering-mathematics
random-variable
0
votes
2
answers
15
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 $4$.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
696
views
probability
gravner
engineering-mathematics
random-variable
normal-distribution
0
votes
1
answer
16
Probability- Gravner- 75.c
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
131
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
17
Probability- Gravner- 75.b
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
136
views
probability
gravner
engineering-mathematics
random-variable
0
votes
2
answers
18
Probability- Gravner- 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
401
views
gravner
probability
engineering-mathematics
random-variable
normal-distribution
4
votes
2
answers
19
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?
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
534
views
probability
gravner
engineering-mathematics
random-variable
normal-distribution
0
votes
1
answer
20
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.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
275
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
21
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 $R$.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
82
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
22
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?
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
120
views
probability
gravner
engineering-mathematics
random-variable
0
votes
0
answers
23
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
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
113
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
24
Probability - Gravner-69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
149
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
25
Probability - Gravner-69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
165
views
probability
gravner
engineering-mathematics
random-variable
0
votes
1
answer
26
Probability - Gravner-69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
Pooja Khatri
asked
in
Probability
Sep 26, 2018
by
Pooja Khatri
133
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
27
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's ... of the randomly chosen group. Let EY= $\mu$ and Var(Y) = $\sigma$2 . Express EX with s, n, $\mu$ and $\sigma$.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
145
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
28
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).
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
178
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
29
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.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
108
views
gravner
probability
engineering-mathematics
random-variable
0
votes
0
answers
30
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 $Y$.
Pooja Khatri
asked
in
Probability
Sep 25, 2018
by
Pooja Khatri
111
views
gravner
probability
engineering-mathematics
random-variable
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