The p.d.f. of a continuous random variable $X$ is given by $f(x) = \frac{x}{8}$ for $0 < x < 4$ and $f(x) = 0$ otherwise. Then $P(X \leq 2)$ is:

Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.

If the probability that an individual will suffer a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ individuals suffer a bad reaction is

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

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.15$	$0.23$	$k$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$, then $P(E \cup F) = $

For the probability distribution given below,find $\operatorname{Var}(X)$.

$X$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$P(X=x)$	$0.07$	$0.2$	$0.3$	$k$	$0.07$	$0.04$	$0.02$

An observer counts $240$ vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows a Poisson distribution, the probability that more than two vehicles arrive over a $30 \text{ sec}$ time interval is