Find the mean of the probability distribution of the random variable X, which can take only the values 2,3,4,5 given that p(2)= 2/7, P(3)= 3/7, P(4) = 1/7, and P(5)= 1/7.

The mean (the expected value) of a discrete random variable $X$ is the number given by

$\mu =E(X)=\sum x P(x)$$=2(\dfrac{2}{7})+3(\dfrac{3}{7})+4(\dfrac{1}{7})+5(\dfrac{1}{7})=\dfrac{22}{7}$

Therefore, mean of the random variable $X$ is $\dfrac{22}{7}.$