The value of C for which P(x=K) = CK^2 can serve as the probability function of a random variable x that takes values 0, 1, 2, 3, 4 is: - Mathematics MCQ Mathematics Mock Test - 6 2026 | ExamTest.live | ExamTest.live

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The value of C for which P (x = K) = C K^{2} can serve as the probability function of a random variable x that takes values 0, 1, 2, 3, 4 is:

A $1/30$
B $1/10$
C $1/3$
D $1/15$

Solution & Step-by-step Explanation

For a function to be a probability mass function, the sum of probabilities for all possible values must be 1 : K = 0 \sum 4 P (x = K) = 1 C (0^{2}) + C (1^{2}) + C (2^{2}) + C (3^{2}) + C (4^{2}) = 1 C (0 + 1 + 4 + 9 + 16) = 1 30 C = 1 ⟹ C = \frac{1}{30}

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The value of C for which P (x = K) = C K^{2} can serve as the probability function of a random variable x that takes values 0, 1, 2, 3, 4 is:

A

1/30

B

1/10

C

1/3

D

1/15

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