Answer to Question #300391 in Statistics and Probability for Nics

Question

the probabilities that a student gets 0, 1,2,3,4, or 5 mistakes are respectively. What is the average number of mistakes that a student makes in this class? What is expected value, variance and standard deviation of this discrete probability distribution?

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} x & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline p(x) & 0.12 & 0.25 & 0.36 & 0.14 & 0.08 & 0.05 \\ \end{array}$$

$$mean=E(X)=0.12(0)+0.25(1)+0.36(2)$$

$$+0.14(3)+0.08(4)+0.05(5)=1.96$$

$$E(X^2)=0.12(0)^2+0.25(1)^2+0.36(2)^2+0.14(3)^2$$

$$+0.08(4)^2+0.05(5)^2=5.48$$

$$Var(X)=\sigma^2=E(X^2)-(E(X))^2$$

$$=5.48-(1.96)^2=1.6384$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{1.6384}=1.28$$