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] = $

The mean of the numbers obtained on throwing a die having written $1$ on three faces,$2$ on two faces,and $5$ on one face is

For the following probability distribution,find the $Var(X)$.

$X$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X)$	$0.1$	$0.2$	$0.2$	$0.3$	$0.15$	$0.05$

(Given : $(0.25)^2 = 0.0625$,$(0.35)^2 = 0.1225$,$(0.45)^2 = 0.2025$)

The probability distribution of a discrete random variable $X$ is given by the following table:

$X = x$	$0$	$1$	$2$	$3$	$4$
$P(X = x)$	$k$	$2k$	$4k$	$2k$	$k$

Then the value of $P(X \leq 2)$ is:

The random variable $X$ has a probability distribution $P(X)$ of the following form,where $k$ is some number:
$P(X) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$
Find $P(X < 2)$,$P(X \leq 2)$,and $P(X \geq 2)$.

In a game,$3$ coins are tossed. $A$ person is paid ₹ $7$ if he gets all heads or all tails,and he is supposed to pay ₹ $3$ if he gets one head or two heads. The amount he can expect to win on an average per game is ₹