If X is a discrete random variable which assumes values \( x_1,x_2,x_3,\ldots,x_n \) with the respective probabilities \( p_1,\ p_2,\ldots,p_n \) , then
Match the LIST-I with LIST-II
| LIST-I | LIST-II |
| A. \( \sum_{i=1}^{n}p_i= \) | I. \( E(X^2) \) |
| B. \( \sum_{i=1}^{n}p_ix_i= \) | II. \( Var(X) \) |
| C. \( \sum_{i=1}^{n}p_ix_i^2= \) | III. 1 |
| D. \( E(X^2)-\{E(X)\}^2= \) | IV. \( E(X) \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-III, B-IV, C-I, D-II
(A) \( \sum_{i=1}^{n}p_i= \)
This matches III. 1. The probabilities of all the values add up to 1.
(B) \( \sum_{i=1}^{n}p_ix_i= \)
This matches IV. \( E(X) \). This is the definition of the mean (expectation).
(C) \( \sum_{i=1}^{n}p_ix_i^2= \)
This matches I. \( E(X^2) \). This is the expectation of \( X^2 \).
(D) \( E(X^2)-\{E(X)\}^2= \)
This matches II. \( Var(X) \). This is the formula for the variance.
So the matching is A-III, B-IV, C-I, D-II.