![Show that if X has a normal distribution with parameters n and m, then Y = aX+ b( a linear
function of X) also has a normal distribution. What are the parameters of the distribution of
Y(i.e.: E[Y] and Var[Y])?
Solution
If X~N(n,m) i.e. E[X]=n and Var(X)=m then aX+b will have E[aX+b] =aE[X]+b =
an+b and Var(aX+b) = a^2Var(X)=a^2m, so that aX+b ~N(an+b,a^2m).](https://image.slidesharecdn.com/showthatifxhasanormaldistributionwithparametersnandmth-230327083649-2faf2a2a/85/Show-that-if-X-has-a-normal-distribution-with-parameters-n-and-m-th-pdf-1-320.jpg)
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Show that if X has a normal distribution with parameters n and m, th.pdf
- 1. Show that if X has a normal distribution with parameters n and m, then Y = aX+ b( a linear function of X) also has a normal distribution. What are the parameters of the distribution of Y(i.e.: E[Y] and Var[Y])? Solution If X~N(n,m) i.e. E[X]=n and Var(X)=m then aX+b will have E[aX+b] =aE[X]+b = an+b and Var(aX+b) = a^2Var(X)=a^2m, so that aX+b ~N(an+b,a^2m).