From a lot of $20$ baskets,which includes $6$ defective baskets,a sample of $2$ baskets is drawn at random one by one without replacement. The expected value of the number of defective baskets is

The p.d.f. of a continuous random variable $X$ is given by $f(x) = \frac{x+2}{18}$ for $-2 < x < 4$ and $f(x) = 0$ otherwise. Then $P[|x| < 1] = $

$A$ boy rolls a die once. If an even number appears, the number of chocolates the boy gets is equal to two more than the number that appeared. If an odd number appears on the die, the number of chocolates he gets is equal to three more than the number that appeared. If a random variable $X$ represents the number of chocolates the boy receives, then the range of $X$ is:

The cumulative distribution function $F(X)$ of a discrete random variable $X$ is given by the following table:

$X$	$1$	$2$	$3$	$4$	$5$	$6$
$F(X=x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

Then $P[X=4] + P[X=5] = $

An unbiased coin is tossed $5$ times. Suppose that a variable $X$ is assigned the value $k$ when $k$ consecutive heads are obtained for $k=3, 4, 5$; otherwise,$X$ takes the value $-1$. Then the expected value of $X$ is:

If the probability function of a random variable $X$ is defined by $P(X=k) = a \left( \frac{k+1}{2^k} \right)$ for $k = 0, 1, 2, 3, 4, 5$,then the probability that $X$ takes a prime value is