Question

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 $0,1,2,3,4$ is

• A. $\frac{1}{30}$
• B. $\frac{1}{10}$
• C. $\frac{1}{3}$
• D. $\frac{1}{15}$

Answer 1

The correct option is A

$\frac{1}{30}$

Explanation for the correct option:

Find the value of $C$

It is given that, $P(X=k)=C{k}^2$ can serve as the probability function of a random variable $X$ that takes $0,1,2,3,4$.

We know that the sum of all the possibilities is $1$.

Therefore,

$$\begin{gathered} C\left[0^2+1^2+2^2+3^2+4^2\right]=1 \\ \Rightarrow C\left[0+1+4+9+16\right]=1 \\ \Rightarrow C\left[30\right]=1 \\ \Rightarrow C=\frac{1}{30} \end{gathered}$$

Therefore, 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 $0,1,2,3,4$ is $\frac{1}{30}$.

Hence, option A is correct .