For the probability distribution given by following

Var(X) =

A random variable X has the following probability distribution

Then $$\mathrm{P}(3<\mathrm{x} \leq 6)=$$

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

The distribution function $$F(X)$$ of discrete random variable $$X$$ is given by

Then $$\mathrm{P[X=4]+P[x=5]=}$$