random variable

The random variable X takes values in {-1,0,1} with probabilities P(X = -1) = P(X = 1) = α and P(X = 0) = 1 − 2α, where 0 < α < 1/2. Let g(α) denote the entropy of X (in bits), par...

Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained. The expectation of $X$ is ___________ (roun...

A random variable X, distributed normally as N(0,1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is (In the option...

The two sides of a fair coin are labelled as 0 and 1 . The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses....

$X$ is a random variable with uniform probability density function in the interval $[-2,10]$. For $Y=2 X-6$, the conditional probability $P(Y \leq 7 \mid X \geq 5)$ (rounded off to...

A random variable X takes values -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the c...

The variance of a random variable X is $$\sigma _x^2\,.$$ Then the variance of - kx (where k is a positive constant ) is