A coin is tossed three times.

Question

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:

Accepted Answer

Outcome
    $x_i$
    $p_i$

HHH
    0
    $\frac{1}{8}$

TTT
    0
    $\frac{1}{8}$

HHT
    1
    $\frac{1}{8}$

HTH
    1
    $\frac{1}{8}$

THH
    0
    $\frac{1}{8}$

TTH
    0
    $\frac{1}{8}$

THT
    1
    $\frac{1}{8}$

HTT
    1
    $\frac{1}{8}$

$\begin{aligned} & \mu=\sum x_i P_i=\frac{1}{2} \ & \sigma^2=\sum x_i^2 P_i-\mu^2 \ & =\frac{1}{2}-\frac{1}{4}=\frac{1}{4} \ & 64\left(\mu+\sigma^2ight)=64\left[\frac{1}{2}+\frac{1}{4}ight] \ & =64 	imes \frac{3}{4}=48\end{aligned}$

Solutions · 1