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Recent questions tagged gravner
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1
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?
asked
Oct 23, 2019
in
Probability
by
ajaysoni1924
Boss

127
views
gravner
probability
engineeringmathematics
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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 $0.99$?
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

81
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probability
gravner
engineeringmathematics
randomvariable
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votes
1
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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 $10$ %
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

76
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probability
gravner
engineeringmathematics
randomvariable
0
votes
1
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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 $EM$.
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

83
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gravner
probability
engineeringmathematics
randomvariable
+1
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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 $0.99$.
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

51
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probability
gravner
engineeringmathematics
randomvariable
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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 ?
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

53
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probability
gravner
engineeringmathematics
randomvariable
+1
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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 $M$.
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

57
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probability
gravner
engineeringmathematics
randomvariable
uniformdistribution
0
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1
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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?
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

63
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probability
gravner
engineeringmathematics
randomvariable
uniformdistribution
0
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1
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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 $8.20$.
asked
Sep 27, 2018
in
Probability
by
Pooja Khatri
Boss

67
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probability
gravner
engineeringmathematics
randomvariable
uniformdistribution
0
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1
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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 $Y$ $=$ $X^2$
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

74
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probability
gravner
engineeringmathematics
randomvariable
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0
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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 $\text{E(1/X)}$.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

33
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probability
gravner
engineeringmathematics
randomvariable
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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.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

51
views
gravner
probability
engineeringmathematics
randomvariable
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 $90$%?
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

48
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probability
gravner
engineeringmathematics
randomvariable
0
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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 $n= 1000$.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

25
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probability
gravner
engineeringmathematics
randomvariable
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2
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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 $4$.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

205
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probability
gravner
engineeringmathematics
randomvariable
normaldistribution
0
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1
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16
Probability Gravner 75.c
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

41
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
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17
Probability Gravner 75.b
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

40
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
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18
Probability Gravner 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

64
views
gravner
probability
engineeringmathematics
randomvariable
normaldistribution
+2
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1
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19
Probability  Gravner74
Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ > $0$. How is $Y$ distributed?
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

159
views
probability
gravner
engineeringmathematics
randomvariable
normaldistribution
0
votes
1
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20
Probability  Gravner73
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.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

62
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
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21
Probability  Gravner72
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 $R$.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

16
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
22
Probability  Gravner71
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?
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

28
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
0
answers
23
Probability  Gravner70
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= 1X4
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

18
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
24
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

53
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
25
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

55
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
26
Probability  Gravner69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
asked
Sep 26, 2018
in
Probability
by
Pooja Khatri
Boss

42
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gravner
probability
engineeringmathematics
randomvariable
0
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27
Probability  Gravner68.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 $\sigma$.
asked
Sep 25, 2018
in
Probability
by
Pooja Khatri
Boss

26
views
gravner
probability
engineeringmathematics
randomvariable
0
votes
0
answers
28
Probability  Gravner68.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).
asked
Sep 25, 2018
in
Probability
by
Pooja Khatri
Boss

22
views
gravner
probability
engineeringmathematics
randomvariable
0
votes
0
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29
Probability  Gravner68.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.
asked
Sep 25, 2018
in
Probability
by
Pooja Khatri
Boss

20
views
gravner
probability
engineeringmathematics
randomvariable
0
votes
0
answers
30
Probability  Gravner68.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 $Y$.
asked
Sep 25, 2018
in
Probability
by
Pooja Khatri
Boss

26
views
gravner
probability
engineeringmathematics
randomvariable
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