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Let Z be standard normal. Compute density for the random variable 3.pdf

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Let Z be standard normal. Compute density for the random variable 3Z+4 Solution Since Z~Normal(mean=0, s^2=1) (standard normal) So 3Z+4~Normal(mean=7, s^2=9) ---------------------------------------------------- E(Z)=1 E(3Z+4)=3*E(Z)+4=3+4=7 ----------- -------------------------------------------- Var(Z)=1 Var(3Z+4)=9Var(Z)=9*1=9.

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Let Z be standard normal. Compute density for the random variable 3Z+4 Solution Since Z~Normal(mean=0, s^2=1) (standard normal) So 3Z+4~Normal(mean=7, s^2=9) ---------------------------------------------------- E(Z)=1 E(3Z+4)=3*E(Z)+4=3+4=7 ----------- -------------------------------------------- Var(Z)=1 Var(3Z+4)=9Var(Z)=9*1=9

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Let Z be standard normal. Compute density for the random variable 3.pdf

  • 1. Let Z be standard normal. Compute density for the random variable 3Z+4 Solution Since Z~Normal(mean=0, s^2=1) (standard normal) So 3Z+4~Normal(mean=7, s^2=9) ---------------------------------------------------- E(Z)=1 E(3Z+4)=3*E(Z)+4=3+4=7 ----------- -------------------------------------------- Var(Z)=1 Var(3Z+4)=9Var(Z)=9*1=9