Q4 Comprehension 3 Marks 21 Dec 2025
Passage
Suppose X X X is a binomial random variable with parameters n = 10 n = 10 n = 10 and p = 1 4 p = \frac{1}{4} p = 4 1 . Define a new random variable Y = X + 10 Y = X + 10 Y = X + 10 . Based on the above data, answer the given subquestions.
Find the PMF of Y.
A P ( Y = k ) = ( 10 k − 10 ) ( 1 / 4 ) k − 10 ( 3 / 4 ) 20 − k , for k = 10 , 11 , 12 , . . . , 20. P(Y = k) = \binom{10}{k-10} (1/4)^{k-10} (3/4)^{20-k}, \quad \text{for } k = 10, 11, 12, ..., 20. P ( Y = k ) = ( k − 10 10 ) ( 1/4 ) k − 10 ( 3/4 ) 20 − k , for k = 10 , 11 , 12 , ... , 20. B P ( Y = k ) = ( 10 k − 10 ) ( 1 / 4 ) ( 3 / 4 ) 20 − k , for k = 10 , 11 , 12 , . . . , 20. P(Y = k) = \binom{10}{k-10} (1/4) (3/4)^{20-k}, \quad \text{for } k = 10, 11, 12, ..., 20. P ( Y = k ) = ( k − 10 10 ) ( 1/4 ) ( 3/4 ) 20 − k , for k = 10 , 11 , 12 , ... , 20. C P ( Y = k ) = ( 10 k ) ( 1 / 4 ) k ( 3 / 4 ) 10 − k , for k = 0 , 1 , 2 , . . . , 10. P(Y = k) = \binom{10}{k} (1/4)^k (3/4)^{10-k}, \quad \text{for } k = 0, 1, 2, ..., 10. P ( Y = k ) = ( k 10 ) ( 1/4 ) k ( 3/4 ) 10 − k , for k = 0 , 1 , 2 , ... , 10. D P ( Y = k ) = ( 20 k − 10 ) ( 1 / 4 ) k − 10 ( 3 / 4 ) 20 − k , for k = 10 , 11 , 12 , . . . , 20. P(Y = k) = \binom{20}{k-10} (1/4)^{k-10} (3/4)^{20-k}, \quad \text{for } k = 10, 11, 12, ..., 20. P ( Y = k ) = ( k − 10 20 ) ( 1/4 ) k − 10 ( 3/4 ) 20 − k , for k = 10 , 11 , 12 , ... , 20. 