Two balls are drawn at random from a bag containing $5$ black balls and $3$ white balls. If the random variable $X$ denotes the number of white balls drawn, then the mean of $X$ is

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

If $X$ is a Poisson variate such that $P(X=2)=P(X=3)$,then $e^3 P(X=4)$ is

$A$ student studies for $X$ number of hours during a randomly selected school day. The probability distribution of $X$ is given by the following form,where $k$ is a constant:
$P(X=x) = \begin{cases} 0.2, & \text{if } x=0 \\ kx, & \text{if } x=1 \text{ or } 2 \\ k(6-x), & \text{if } x=3 \text{ or } 4 \\ 0, & \text{otherwise} \end{cases}$
The probability that the student studies for at most two hours is:

$A$ six-faced fair die is thrown until $2$ appears. What is the probability that $2$ appears in an even number of trials? (The die has six faces numbered $1, 2, 3, 4, 5,$ and $6$.)

If $X$ is a Poisson variate such that $P(X=1)=P(X=2)$,then $P(X=4)$ is equal to