Find the variance of the number obtained on a throw of a fair die.

If the probability function of a random variable $X$ is given by $P(X=j) = \frac{1}{2^j}$ for $j = 1, 2, 3, \ldots, \infty$,then the variance of $X$ is:

$A$ manufacturing company noticed that $1 \%$ of its products are defective. If a dealer orders for $300$ items from this company,then the probability that the number of defective items is at most one is

$A$ random variable $X$ has the following probability distribution:
$X = 1, 2, 3, 4, 5$
$P(X) = 0.1, 0.2, 0.3, 0.2, 0.2$
For the events $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$, find $P(E \cap F)$.

$A$ 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:

From a lot of $12$ items containing $3$ defectives,a sample of $5$ items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $X$ is $\frac{m}{n}$,where $\operatorname{gcd}(m, n)=1$,then $n-m$ is equal to..........