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Question: The value of C for which P(X=k) = Ck<sup>2</sup> can serve as the probability function of a random v...

The value of C for which P(X=k) = Ck2 can serve as the probability function of a random variable X that takes 0, 1, 2, 3, 4 is

A

1/30

B

1/10

C

1/3

D

1/5

Answer

1/30

Explanation

Solution

∑k=04P(X=k)=1 6mu⇒ 6mu∑k=04Ck2=1\sum_{k = 0}^{4}{P(X = k) = 1\mspace{6mu} \Rightarrow \mspace{6mu}\sum_{k = 0}^{4}{Ck^{2} = 1}}

⇒ C(12 + 22 + 32 +42) = 1 ⇒ C = 1/30