Zhejiang University of Science and Techmology 3. Let the pmf of a discrete rv X be...

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Zhejiang University of Science and Techmology 3. Let the pmf of a discrete rv X be Mark 0.2 0.3 0.1 0.4 And Y=2x2+1, Find the prnf of Y. Eor) and Var(r). .

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$y-1 Hence P(y = 1) = P(X = 0) = 0.3. P(y = 3) = P(X = 1)+ P(X =-1) = 0.3. P(y = 9) = P(X = 2) = 0.4 since P(X =-2) = 0 pm f of Y is 0.3 u,hen y= 1 P(Y -y)o.3 when y -3 0.4 when y 9 E(Y)0.3+3*0.3+9*0.4 4.8 E(Y2) 12 * 0.34 32 * 0.34 92 * 0.4-35.4 Var (Y) = E(Y2)-E2(Y) = 35.4-4.82-12.36$

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