If the probability that the random variable $X$ takes values $x$ is given by $P(X = x) = k(x + 1)3^{-x}$ for $x = 0, 1, 2, 3, \ldots$,where $k$ is a constant,then $P(X \geq 2)$ is equal to

$A$ random variable $X$ assumes values $1, 2, 3, \ldots, n$ with equal probabilities. If the ratio of the variance of $X$ to the expected value of $X$ is equal to $4$,then the value of $n$ is:

$A$ random variable $X$ takes values $0, 1, 2, 3$ with probabilities $\frac{2a + 1}{30}, \frac{8a - 1}{30}, \frac{4a + 1}{30}, b$ respectively, where $a, b \in R$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of $X$ such that $\sigma^{2} + \mu^{2} = 2$. Then $\frac{a}{b}$ is equal to:

If the function $P[X = x] = \begin{cases} \frac{K \cdot 2^x}{x!}, & x = 0, 1, 2, 3 \\ 0, & \text{otherwise} \end{cases}$ forms a probability mass function (p.m.f.),then the value of $K$ is:

If the probability distribution of a random variable $X$ is as follows,then $k=$

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$4k$	$3k$	$k$

(in $/10$)

Which of the following functions is not a probability density function $(p.d.f.)$ of a continuous random variable $X$?