Let f(x) = cx^2 for x = 1, 2, 3 . The value of constant c such that f satisfies the conditions of being a probability mass function (PMF) is: - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live | ExamTest.live

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Let f (x) = c x^{2} for x = 1, 2, 3 . The value of constant c such that f satisfies the conditions of being a probability mass function (PMF) is:

A $1/11$
B $1/12$
C $1/13$
D $1/14$

Solution & Step-by-step Explanation

For f (x) to be a PMF, the sum of all probabilities must be 1. x = 1 \sum 3 f (x) = 1 f (1) + f (2) + f (3) = 1 c (1)^{2} + c (2)^{2} + c (3)^{2} = 1 c (1 + 4 + 9) = 1 14 c = 1 ⟹ c = \frac{1}{14}

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Let f (x) = c x^{2} for x = 1, 2, 3 . The value of constant c such that f satisfies the conditions of being a probability mass function (PMF) is:

A

1/11

B

1/12

C

1/13

D

1/14

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Probability Random Variables PMF

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