Question

The following table shows the probability distribution for a discrete random variable.

The mean of the discrete random variable X is 19.59. What is the variance of X? Round your answer to the nearest hundredth.

Answer 1

the table is

x 12 15 17 20 22 24 25 30
--------------------------------------------
P(x) .07 .21 .17 .25 .05 .04 .13 .08

Answer 2

\[Var(X) = E(X^2)-[E(X)]^2\]
The problem already gives you E(X), so you just need to find E(X^2) as follows:
\[E(X^2)=\sum_{x}x^2*P(x)\]
So: \[E(X^2)=12^2(0.7)+15^2(0.21)+...+30^2(0.8)\]
Once you find the value of E(X^2), just do \[Var(X)=E(X^2)-[E(X)]^2=E(X^2)-(19.59)^2\]