Question

Let a coin is tossed thrice. Let the random variable x is tail follows head. Let the mean of x is \(\mu\) and variance is \(\sigma^2.\) Find \(64\left(\mu+\sigma^2\right).\)

(1) 48

(2) 64

(3) 132

(4) 128

Answer 1

Correct option is (1) 48

\(\mu=\Sigma P_i x_i=\frac{1}{2} \)  

\(\sigma^2=\Sigma P_i x_i^2-\mu^2 \)  

\(=\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \)  

\(64\left(\frac{1}{2}+\frac{1}{4}\right)=64 \times \frac{3}{4}=48\)