Match List-I with List-II
| List-I (random variable) | List-II (expected value) | ||
| (A) | The number of tails in one toss of a fair coin | (I) | \(\displaystyle\frac{3}{2}\) |
| (B) | The number shown when a fair four-faced die, with faces numbered 1, 2, 3 and 4, is thrown once | (II) | \(\displaystyle\frac{7}{2}\) |
| (C) | The number of sixes in 9 throws of a fair die | (III) | \(\displaystyle\frac{1}{2}\) |
| (D) | The number of accidents in a week at a crossing where the number of accidents in a day is a Poisson variate with mean 0.5 | (IV) | \(\displaystyle\frac{5}{2}\) |
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) The number of tails in one toss of a fair coin
This matches (III) \(\displaystyle\frac{1}{2}\). X is 0 or 1, each with probability \(\displaystyle\frac{1}{2}\):
\( \displaystyle E(X) = 0 \times \frac{1}{2} + 1 \times \frac{1}{2} = \frac{1}{2} \)
(B) The number shown by the four-faced die
This matches (IV) \(\displaystyle\frac{5}{2}\). Each of 1, 2, 3, 4 has probability \(\displaystyle\frac{1}{4}\):
\( \displaystyle E(X) = \frac{1 + 2 + 3 + 4}{4} = \frac{5}{2} \)
(C) The number of sixes in 9 throws
This matches (I) \(\displaystyle\frac{3}{2}\). X is binomial with n = 9, \(\displaystyle p = \frac{1}{6}\):
\( \displaystyle E(X) = np = 9 \times \frac{1}{6} = \frac{3}{2} \)
(D) The number of accidents in a week
This matches (II) \(\displaystyle\frac{7}{2}\). The Poisson mean is proportional to the length of the period, so for 7 days
\( \displaystyle m = 7 \times 0.5 = \frac{7}{2} \)