If $f(x) = \begin{cases} 3(1 - 2x^2) & ; 0 < x < 1 \\ 0 & ; \text{otherwise} \end{cases}$ is a probability density function of $X$,then $P\left(\frac{1}{4} < x < \frac{1}{3}\right)$ is

If $6$ is the mean of a Poisson distribution,then $P(X \geq 3)=$

Let a sample space be $S = \{\omega_{1}, \omega_{2}, \ldots, \omega_{6}\}$. Which of the following assignments of probabilities to each outcome is valid?

Outcome	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$
$(b)$	$1$	$0$	$0$	$0$	$0$	$0$

If $X$ is a Poisson variate such that $P(X=1) = 2P(X=2)$,then $P(X=3)$ is equal to:

At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:

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

$X=x_i$	$0$	$1$	$2$	$3$	$4$
$P(X=x_i)$	$0.4$	$0.3$	$0.1$	$0.1$	$0.1$

Then the variance of $X$ is