Answer to Question #300391 in Statistics and Probability for Nics

Question #300391

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?





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Expert's answer
2022-02-21T16:25:08-0500
x012345p(x)0.120.250.360.140.080.05\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)mean=E(X)=0.12(0)+0.25(1)+0.36(2)

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

E(X2)=0.12(0)2+0.25(1)2+0.36(2)2+0.14(3)2E(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+0.08(4)^2+0.05(5)^2=5.48

Var(X)=σ2=E(X2)(E(X))2Var(X)=\sigma^2=E(X^2)-(E(X))^2

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

σ=σ2=1.6384=1.28\sigma=\sqrt{\sigma^2}=\sqrt{1.6384}=1.28


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