expectation

Let $ x $ and $ y $ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $ z = xy $ and let the mean values of $ x, y, z $ be $ \bar...

Consider the two statements. S 1 : There exist random variables X and Y such that (E[X - E(X)) (Y - E(Y))]) 2 > Var[X] Var[Y] S 2 : For all random variables X and Y, Cov[X, Y] = E...

For any discrete random variable X, with probability mass function P(X = j) = pj, Pj ≥ 0, j∈ {0,...,N}, and $\sum_{j=0}^{N} p_j = 1$, define the polynomial function $g_x(z) = \sum_...

If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X + 2)^2] equals _________.

If a random variable $$X$$ has a Poisson distribution with mean $$5,$$ then the expectation $$E\left[ {{{\left( {X + 2} \right)}^2}} \right]$$ equals _________.

For any discrete random variable $$X,$$ with probability mass function $$P\left( {X = j} \right) = {p_j},$$ $${p_j}\,\, \ge 0,\,j \in \left\{ {0,..........,\,\,\,N} \right\},$$ and...

If the difference between the expectation of the square of a random variable $$\left( {E\left[ {{X^2}} \right]} \right)$$ and the square of the expectation of the random variable $...

Suppose that the expectation of a random variable X is 5. Which of the following statements is true?

Suppose that the expectation of a random variable X is 5. Which of the following statements is true?