Answer to Question #305394 in Statistics and Probability for Baby

Question #305394

find the variance and stand deviatio of the probability distribution of the random variable x, which can take only the values 2,4,5 and 9 given that P(2)=9/10. P(4)=1/20. P(5)= 1/5.P(9)= 3/10

1
Expert's answer
2022-03-04T04:46:32-0500

Check


9/10+1/20+1/5+3/10=29/2019/10+1/20+1/5+3/10=29/20\not=1

Assume that


P(2)=9/20,P(4)=1/20,P(2)=9/20, P(4)=1/20,

P(5)=1/5,P(9)=3/10P(5)= 1/5,P(9)= 3/10

Check


9/20+1/20+1/5+3/10=20/20=19/20+1/20+1/5+3/10=20/20=1


E(X)=2(9/20)+4(1/20)+5(1/5)+9(3/10)E(X)=2(9/20)+4(1/20)+5(1/5)+9(3/10)

=4.8=4.8


E(X2)=22(9/20)+42(1/20)+52(1/5)+92(3/10)E(X^2)=2^2(9/20)+4^2(1/20)+5^2(1/5)+9^2(3/10)

=31.9=31.9

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

=31.9(4.8)2=8.86=31.9-(4.8)^2=8.86

σ=σ2=8.86=2.9766\sigma=\sqrt{\sigma^2}=\sqrt{8.86}=2.9766


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