The cumulative distribution function of a continuous random variable $X$ is given by $F(x) = \frac{\sqrt{x}}{2}$ for $0 \leq x \leq 4$. Then $P[X > 1]$ is

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

$A$ card is drawn from a pack of $52$ playing cards. The card is replaced and the pack is shuffled. If this process is repeated $6$ times,what is the probability that $2$ hearts,$2$ diamonds,and $2$ black cards are drawn?

If the probability distribution function of a random variable $X$ is given as follows:

$X=x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X=x_i)$	$0.2$	$0.3$	$0.15$	$0.25$	$0.1$

Then $F(0)$ is equal to:

$A$ 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) = $

Let the mean and standard deviation of the probability distribution given by the table below be $\mu$ and $\sigma$ respectively. If $\sigma - \mu = 2$,then find the value of $\sigma$.

$X=x$	$-3$	$0$	$1$	$\alpha$
$P(X=x)$	$\frac{1}{4}$	$K$	$\frac{1}{4}$	$\frac{1}{3}$