JEE Mains · Maths · STD 12 - 13. probability
A coin is tossed three times. Let \(X\) denote the number of times a tail follows a head. If \(\mu\) and \(\sigma^2\) denote the mean and variance of \(X\), then the value of \(64\left(\mu+\sigma^2\right)\) is :
- A \(51\)
- B \(64\)
- C \(32\)
- D \(48\)
Answer & Solution
Correct Answer
(D) \(48\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mu=\sum x_i P_i=\frac{1}{2} \\ & \sigma^2=\sum x_i^2 P_i-\mu^2 \\ & =\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \\ & 64\left(\mu+\sigma^2\right)=64\left[\frac{1}{2}+\frac{1}{4}\right] \\ & =64 \times \frac{3}{4}=48\end{aligned}\)
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