Register
Webpage for Probability

Recent questions tagged probability

4 votes
2 answers
602
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?
User Avatar
0 votes
1 answer
603
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 ...
User Avatar
0 votes
0 answers
604
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 $R$.
User Avatar
0 votes
0 answers
605
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?
User Avatar
0 votes
0 answers
606
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
User Avatar
0 votes
1 answer
607
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).
User Avatar
0 votes
1 answer
608
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 $P(1\leqslant X\leqslant 2)$
User Avatar
0 votes
1 answer
609
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 $c$.
User Avatar
0 votes
0 answers
621
Probability - Gravner-64.d
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (d) Find an expression for $P(Y>10)$.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(d) Find an expression for $P(Y>10)$.
User Avatar
0 votes
0 answers
622
Probability - Gravner-64.c
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (c) Find an expression $P$($X\geqslant 6$).
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(c) Find an expression $P$($X\geqslant 6$)...
User Avatar
0 votes
0 answers
623
Probability - Gravner-64.b
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (b) Write down the probability mass function of Y.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(b) Write down the probability mass functi...
User Avatar
1 votes
0 answers
624
Probability - Gravner-64.a
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (a) Write down the probability mass function of X.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(a) Write down the probability mass functi...
User Avatar
0 votes
0 answers
625
Probability - Gravner-63
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the game repeats. On the average, how many rounds does the game last?
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the ...
User Avatar
0 votes
0 answers
627
Probability - Gravner-61
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
User Avatar
0 votes
0 answers
629
Probability - Gravner-59
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
User Avatar
0 votes
1 answer
630
Probablity-Gravner-58
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
User Avatar
Page: