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:

If $X$ is a Poisson variable such that $3 P(X=4)=\frac{1}{2} P(X=2)+P(X=0)$,then the mean of $X$ is

The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter $\lambda = 6$. The probability that at least one and at most five persons join the queue in a particular minute is:

If random variable $X$ is the waiting time in minutes for a bus and the probability density function of $X$ is given by $f(x) = \begin{cases} \frac{1}{5}, & 0 \leq x \leq 5 \\ 0, & \text{otherwise} \end{cases}$,then the probability of the waiting time being not more than $4$ minutes is = . . . . . . .

If $f(x) = \frac{x}{8}$ for $0 < x < 4$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a continuous random variable $X$,and $F(x)$ is the cumulative distribution function (c.d.f.) associated with $f(x)$,then find $F(0.5)$.

If a variable takes values $0, 1, 2, ..., n$ with frequencies proportional to the binomial coefficients $^nC_0, ^nC_1, ..., ^nC_n$,find the mean of the distribution.