$A$ random variable $X$ has the following probability distribution:

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$0.1$	$0.2$	$0.3$	$0.4$

The mean and standard deviation of $X$ are respectively:

The p.d.f. of a continuous random variable $X$ is $f(x)=\begin{cases} \frac{x^2}{18} & \text{if } -3 < x < 3 \\ 0 & \text{otherwise} \end{cases}$. Then $P[|X| < 2]=$

If a random variable $X$ takes the values $x_1, x_2, x_3, \ldots, x_{100}$ with probability $P(X=x_i) = K i(i+1)$,then $200 K=$

$A$ 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:

$A$ person throws two fair dice. He wins $Rs.\, 15$ for throwing a doublet (same numbers on the two dice),wins $Rs.\, 12$ when the throw results in the sum of $9$,and loses $Rs.\, 6$ for any other outcome on the throw. Then the expected gain/loss (in $Rs.$) of the person is

The probability distribution of a random variable $X$ is given below:

$X=x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X=x)$	$0$	$K$	$2K$	$2K$	$3K$	$K^2$	$2K^2$	$7K^2+K$

Then,$P(0 < X < 5)$ is equal to: