Answer to Question #106583 in Statistics and Probability for Junaid

Question

Compute the mean and variance of the following discrete probability distribution: (Round the final answers to 2 decimal places.)

X P(X)
4 0.4
6 0.1
10 0.5


Mean =
Variance =

Answer 1

$\def\arraystretch{1.5} \begin{array}{c:c} X & P(X) \\ \hline 4 & 0.4 \\ \hdashline 6 & 0.1 \\ \hdashline 10 & 0.5 \end{array}$

$\mu =\sum\limits ^3_{i=1}p(x_i)x_i=0.4\times 4+0.1\times 6+0.5\times 10=7.2$

$\sigma ^2= \sum\limits ^3_{i=1}p(x_i)(x_i-\mu)^2=0.4\times (-3.2)^2+0.1\times (-1.2)^2+0.5\times 2.8^2=8.16$

Answer: mean = 7.2, variance = 8.16.