Recent questions tagged expectation

​​​​​​Suppose $X$ and $Y$ are random variables. The conditional expectation of $X$ given $Y$ is denoted by $E[X \mid Y]$. Then $E[E[X \mid Y]]$ equals$E[X \mid Y]$$\frac{...

​​​​​Let $X=a Z+b$, where $Z$ is a standard normal random variable, and $a, b$ are two unknown constants. It is given that\[E[X]=1, \quad E[(X-E[X]) Z]=-2, \quad E\left[(...

​​​​​​It is given that $P(X \geq 2)=0.25$ for an exponentially distributed random variable $X$ with $E[X]=\dfrac{1}{\lambda}$, where $E[X]$ denotes the expectation of $X$...

A bag contains $5$ white balls and $10$ black balls. In a random experiment, $n$ balls are drawn from the bag one at a time with replacement. Let $S_{n}$ denote the total...

 Each round of a TV game show consists of ten questions. Before each round the host takes ten boxes and places prizes in nine of them, leaving one empty. The host then sh...

Football teams $T_{1}$ and $T_{2}$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other...

A new restaurant chain Burger Paradise has recently opened in Chennai. Burger Paradise offers a variety of burgers, including vegetarian options, as well as sides and dri...

Let $\mathbf{A}=\left(a_{i j}\right)$ be an $m \times n$ matrix such that for $i \in\{1,2, \ldots, m\}$ and $j \in\{1,2, \ldots, n\}$,$a_{i j} \mathrm{~s}$ are real value...

Consider a joint probability density function of two random variables $X$ and $Y$\[f_{X, Y}(x, y)=\left\{\begin{array}{rll}2 x y, & 0<x<2, & 0<y<x \\ 0, & \text { otherwi...