Question

If a random variable \(X\) has a probability mass function \(P(x) = \{\begin{array}{cc}kx^2, & \text{for }x = 1,2,3,4 \\ 0, & \text{otherwise}\end{array}\), then the mean of \(X\) is ...

• A. \(3.232\)
• B. \(2.221\)
• C. \(3.333\)
• D. \(2.222\)

Hint:

Find k from the total probability, then compute the sum of x P(x).

Answer 1

The Correct Option is C

Step 1: Probabilities
$P(1)=\frac1{30}, P(2)=\frac4{30}, P(3)=\frac9{30}, P(4)=\frac{16}{30}$.

Step 2: Weighted sum
$\frac{1\cdot1+2\cdot4+3\cdot9+4\cdot16}{30} = \frac{1+8+27+64}{30} = \frac{100}{30}\approx3.333$. Option (C).

Final Answer:
3.333. \[ \boxed{\text{(C)}\ 3.333} \]