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Given-a-random-variable-X-of-image-set-X-1-1-2-with-probabilities-P-X-1-e-a-P-X-1-e-b-and-P-X-2-e-c-where-a-b-and-c-are-in-an-Arithmetic-Progression-Assuming-the-mathematical-expec

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Question Number 87643 by Ar Brandon last updated on 05/Apr/20
Given a random variable X of image set X(Ω)=[1;−1;2] with probabilities P(X=1)=e^a , P(X=−1)=e^b , and P(X=2)=e^c where a, b, and c are in an Arithmetic Progression. Assuming the mathematical expection E(X) of X is equal to 1. 1∙ Suppose the common difference of the Arithmetic Progression is r a∙ Determine the exact values of the real numbers a, b, and c. b. Show that the variance V(X) of X is equal to ((22)/7).
Givenarandomvariable\boldsymbolXofimagesetX(Ω)=[1;−1;2]withprobabilitiesP(X=1)=ea,P(X=−1)=eb,andP(X=2)=ecwherea,b,andcareinanArithmeticProgression.AssumingthemathematicalexpectionE(X)ofXisequalto1.1⋅SupposethecommondifferenceoftheArithmeticProgressionis\boldsymbolr\boldsymbola⋅Determinetheexactvaluesoftherealnumbersa,b,andc.\boldsymbolb.ShowthatthevarianceV(X)ofXisequalto227.

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