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1
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 ajaysoni1924 219 views
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0 answers
2
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 Pooja Khatri 118 views
0 votes
1 answer
3
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 Pooja Khatri 116 views
0 votes
1 answer
4
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 Pooja Khatri 126 views
1 vote
0 answers
5
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 Pooja Khatri 71 views
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0 answers
6
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 Pooja Khatri 73 views
1 vote
0 answers
7
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) Assume that you know in advance ... . Let $M$ 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 Pooja Khatri 90 views
0 votes
1 answer
8
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 Pooja Khatri 100 views
0 votes
1 answer
9
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 Pooja Khatri 107 views
0 votes
1 answer
10
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 Pooja Khatri 106 views
0 votes
0 answers
11
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 Pooja Khatri 66 views
0 votes
1 answer
12
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 Pooja Khatri 84 views
0 votes
1 answer
13
How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?
asked Sep 26, 2018 in Probability Pooja Khatri 73 views
0 votes
0 answers
14
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 Pooja Khatri 43 views
0 votes
2 answers
15
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 Pooja Khatri 341 views
0 votes
1 answer
16
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 Pooja Khatri 61 views
0 votes
1 answer
17
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 Pooja Khatri 54 views
0 votes
1 answer
18
4 votes
1 answer
19
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 Pooja Khatri 203 views
0 votes
1 answer
20
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 Pooja Khatri 93 views
0 votes
0 answers
21
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 Pooja Khatri 30 views
0 votes
0 answers
22
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 Pooja Khatri 57 views
0 votes
0 answers
23
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
asked Sep 26, 2018 in Probability Pooja Khatri 32 views
0 votes
1 answer
24
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
asked Sep 26, 2018 in Probability Pooja Khatri 75 views
0 votes
1 answer
25
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
asked Sep 26, 2018 in Probability Pooja Khatri 75 views
0 votes
1 answer
26
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
asked Sep 26, 2018 in Probability Pooja Khatri 60 views
0 votes
0 answers
27
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 ... the size 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 Pooja Khatri 40 views
0 votes
0 answers
28
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 Pooja Khatri 38 views
0 votes
0 answers
29
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 Pooja Khatri 32 views
0 votes
0 answers
30
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. (a) Write down the probability mass functions for $X$ and $Y$.
asked Sep 25, 2018 in Probability Pooja Khatri 38 views
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