A continuous random variable $X$ has probability density function $f (x) = 2 x$ for $0 \leq x \leq 1$ , and 0 elsewhere. Then $Pr (X \leq 0.5) =$

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The random variable $X$ has a binomial distribution $X \sim Bi (n = 10, p = 0.2)$ . The standard deviation of $X$ is:
Let $Z \sim N (0, 1)$ . Given that $Pr (Z > 1.2) = 0.1151$ , find $Pr (- 1.2 < Z < 1.2)$ .
A discrete random variable $Y$ has probability function $Pr (Y = y) = k (y + 1)$ for $y \in {0, 1, 2, 3}$ . Find the exact value of $k$ .
Given that events $A$ and $B$ are independent with $Pr (A) = 0.4$ and $Pr (B) = 0.5$ , find $Pr (A^{'} \cup B^{'})$ .
The weights of newborn puppies are normally distributed with mean $500 g$ and standard deviation $40 g$ . If $10%$ of puppies…
A continuous random variable $X$ has probability density function $f (x) = \frac{3}{8} x^{2}$ for $0 \leq x \leq 2$ , and $0$ elsewhere. Calculate…