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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?
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 firs...
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3
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 $0.99$?
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...
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4
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 $10$ %
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 probabi...
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5
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 $EM$.
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6
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...
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7
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...
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11
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 ...
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12
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 $\text{E(1/X)}$.
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13
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.
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14
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 $90$%?
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2 answers
16
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 $4$.
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17
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 $\sigma$ ?
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18
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 $\sigma$ ?
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19
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 $\sigma$ ?
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4 votes
2 answers
20
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?
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1 answer
21
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 ...
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22
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 $R$.
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23
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?
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24
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
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25
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).
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26
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 $P(1\leqslant X\leqslant 2)$
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27
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 $c$.
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