expectation

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 ________ (rounded off...

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...

If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = _________.

Consider a random process $$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$ where the random phase $$\varphi $$ is uniformly distributed in the interval $$\l...

Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mean values of $$X$$ and $${{X^2}}$$, respectively. The relatio...

Let $$X$$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $$100.$$ The expectation, $$E\left[ X \right],$$ is __________.

The power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f \right| \le W} \cr {0,\left| f \r...

If $$E$$ denotes expectation, the variance of a random variable $$X$$ is given by

If E denotes expectation, the variance of a random variable X is given by