Recent questions tagged goclasses_da_probability_wq6

Let $X_{1}, X_{2}, X_{3}$ be independent random variables uniformly distributed on the interval $[0,1]$. Define$$Y=X_{1}+X_{2}+X_{3}$$What is the value of$\mathbb{P}\left...

Let $\mathbb{X}$ and $\mathbb{Y}$ be two independent random variables such that:$\mathbb{X} \sim \operatorname{Exponential}\left(\lambda_{1}\right)$$\mathbb{Y} \sim \oper...

At a busy airport, the time $Y$ (in minutes) an airplane waits for takeoff clearance is modeled as:$$Y=3 X-2$$This waiting time depends on another variable $X$, which fol...

The joint probability mass function (p.m.f.) of the discrete random variables $X, Y, Z$ is given by:$$P(X=x, Y=y, Z=z)= \begin{cases}\frac{1}{4}, & \text { if }(x, y, z) ...

Suppose the joint probability density function (p.d.f.) of random variables $X$ and $Y$ is given by $f_{X, Y}(x, y)= \begin{cases}15 x y^2 & \text...

Consider a random vector ( $X, Y$ ) such that $Y \sim \operatorname{Uniform}(0,1)$ and the conditional distribution of $X$ given that $Y=y$ is Normal with mean $y^{2}$ an...

Let $X, Y, Z$ be random variables such that $\operatorname{cov}(X, Y)=1, \operatorname{cov}(X, Z)=-2$, $\operatorname{cov}(Y, Z)=3$, and $V(Z)=5$. What's $\operatorname{c...

Let $X$ and $Y$ be jointly Gaussian random variables with the following parameters:$$\mu_{X}=0, \quad \mu_{Y}=0, \quad \sigma_{X}^{2}=1, \quad \sigma_{Y}^{2}=4, \quad \rh...

$X$ and $Y$ are two jointly distributed random variables. The conditional mean and variance of $Y$ given $X$ are given by $3 X$ and $9 X$. The unconditional mean and vari...

Let $X$ and $Y$ be continuous random variables with joint PDF: $f_{X, Y}(x, y)= \begin{cases}k & \text { if } 0<y \leq x \leq 1 \\ 0 & \text...

Suppose $U_{1}$ and $U_{2}$ are i.i.d. $\mathrm{U}(0,1)$ random variables. Furthermore, let $X$ be a$\operatorname{Bin}(2,0.5)$ random variable that is independent of $\l...

Suppose $X$ is a random variable with finite variance. For $0<\theta<1$ and $n>3$, let $X_{1}=X$, $X_{2}=\theta X_{1}, X_{3}=\theta X_{2}, \ldots, X_{n}=\theta X_{n-1}$. ...

Let $X$ be a continuous random variable with probability density function ...

Let the random variable $X \sim B(5, p)$ such that $P(X=2)=2 P(X=3)$. Then the variance of $X$ is$\frac{10}{3}$ $\frac{10}{9}$ $\frac{5}{3}$ $\frac{5}{9}$

Let $X$ and $Y$ be independent $\operatorname{Bin}\left(3, \frac{1}{3}\right)$ random variables. Then the probability that the matrix$$P=\left(\begin{array}{cc}\frac{X}{\...