Two cards are drawn at random from a box which contains $5$ cards numbered $1, 1, 2, 2, 3$. If $X$ denotes the sum of the numbers on the two cards, then the expected value of $X$ is...

If the error involved in making a certain measurement is a continuous random variable $X$ with probability density function $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ and $f(x) = 0$ otherwise,then $P[-1 < X < 1] = $

If the p.m.f. of a random variable $X$ is given by $P(X=x) = \frac{\binom{5}{x}}{2^{5}}$ for $x = 0, 1, 2, \ldots, 5$ and $0$ otherwise,then which of the following is not true?

$A$ random variable $X$ has the following probability distribution:
$X = 1, P(X) = 0.15$
$X = 2, P(X) = 0.20$
$X = 3, P(X) = 0.25$
$X = 4, P(X) = 0.30$
$X = 5, P(X) = 0.10$
For the event $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$, find $P(E \cup F)$.

On an average,if one out of $100$ electric bulbs produced by a company is found to be defective,then the probability that there are at least two defective bulbs in a consignment of $600$ bulbs is:

The probability distribution of a random variable $X$ is given by

$X = x$	$0$	$1$	$2$
$P(X = x)$	$\frac{1}{5}$	$\frac{2}{5}$	$\frac{2}{5}$

Then the variance of $X$ is