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Classical Definition of Probability

The value of ...

Question

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

\frac{1}{30}

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\frac{1}{10}

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\frac{1}{3}

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\frac{1}{15}

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Solution

The correct option is A $\frac{1}{30}$
$4 \sum k = 0 P (X = k) = 1 \Rightarrow 4 \sum k = 0 c k^{2} = 1$
$\Rightarrow c (1^{2} + 2^{2} + 3^{2} + 4^{2}) = 1 \Rightarrow c = \frac{1}{30}$

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