Let a pair of dice be thrown and the random variable $X$ be the sum of the numbers that appear on the two dice. Find the mean or expectation of $X$.

India plays two matches each against Australia and West Indies. The probabilities of India scoring $0, 1,$ and $2$ points in a match are $0.45, 0.05,$ and $0.50$ respectively. Assuming the results are independent,what is the probability that India scores at least $7$ points?

If the range of a random variable $X$ is $\{0, 1, 2, 3, 4, \ldots\}$ with $P(X=k) = \frac{(k+1)a}{3^k}$ for $k \geq 0$,then $a$ is equal to

If the probability that an individual will suffer a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ individuals suffer a bad reaction is

If $X$ is a Poisson variate such that $P(X=1) = 2P(X=2)$,then $P(X=3)$ is equal to:

Suppose three coins are tossed simultaneously. If $X$ denotes the number of heads,then the probability distribution of $X$ is: