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
|
$X$ |
1 |
2 |
3 |
4 |
|
$P(X)$ |
$\frac{1}{3}$ |
$\frac{1}{6}$ |
$\frac{1}{5}$ |
$\frac{3}{10}$ |
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:
Answer & explanation
Correct answer: option 2
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.