Question

let (x) be a random variable with the following probability distribution.

\

$$\begin{tabular}{|c|c|} \\hline value (x) of (x) & (p(x=x)) \\\\ \\hline 40 & 0.25 \\\\ \\hline 50 & 0.10 \\\\ \\hline 60 & 0.05 \\\\ \\hline 70 & 0.20 \\\\ \\hline 80 & 0.40 \\\\ \\hline \\end{tabular}$$

complete the following. (if necessary, consult a list of formulas.)

(a) find the expectation (e(x)) of (x).
(e(x) = )

(b) find the variance (\text{var}(x)) of (x).
(\text{var}(x) = )

Explanation:

Calculate the expected value of X

Using the Expected Value Calculation knowledge point

$$
LATEXBLOCK0
$$

Calculate the expected value of X squared

Using the Variance of Random Variable knowledge point

$$
LATEXBLOCK1
$$

Calculate the variance of X

Using the Variance of Random Variable knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question (a)

\(E(X) = 64\)

Question (b)

\(\operatorname{Var}(X) = 274\)