Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).

Assertion (A): If a random variable X has the following probability distribution

then the mean of the probability distribution is $\frac{37}{15}$.

Reason (R): Variance of the probability distribution = $∑p_i{x_i}^2-(∑p_ix_i)^2$ where x's represent the values of a random variable and ${p_i}'s$ represent the probabilities of ${x_i}'s$.

Select the correct answer from the options given below:

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

The correct answer is Option (2) → Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Mean (μ) = $∑p_ix_i = p_1x_1 + p_2x_2 + p_3x_3 + p_4x_4$

$=\frac{1}{3}×1+\frac{1}{6}×2+\frac{1}{5}×3+\frac{3}{10}×4$

$=\frac{1}{3}+\frac{1}{3}+\frac{3}{5}+\frac{6}{5}$

$=\frac{5+5+9+18}{15}=\frac{37}{15}$

∴ Assertion is true.

Also, Reason is true.

Reason is not the correct explanation of Assertion.