If the mean of a Poisson distribution is $\frac{1}{2}$, then the ratio of $P(X=3)$ to $P(X=2)$ is

If a random variable $X$ has the probability distribution given by $P(X=0)=3C^3$,$P(X=2)=5C-10C^2$ and $P(X=4)=4C-1$,then the variance of that distribution is

In a city,it is found that $10$ accidents took place in a span of $50$ days. Assuming that the number of accidents follows the Poisson distribution,the probability that there will be $3$ or more accidents in a day in that city is

$A$ random variable $X$ has the following probability distribution:
$X = 1, P(X) = 0.15$
$X = 2, P(X) = 0.20$
$X = 3, P(X) = 0.25$
$X = 4, P(X) = 0.30$
$X = 5, P(X) = 0.10$
For the event $E = \{ X \text{ is a prime number} \}$ and $F = \{ X < 4 \}$, find $P(E \cup F)$.

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

The range of a random variable $X$ is $\{1, 2, 3, \ldots\}$ and $P(X=x) = \frac{c^x}{x!}$ for $x = 1, 2, 3, \ldots$. Then the value of $c$ is