Finding Constants for a Gaussian PDF

[ahamdiheme]

Homework Statement

The exam grades in a certain class have a Gaussian PDF with mean m and standard deviation \sigma. Find the constants a and b so that the random variable y=aX+b has a Gaussian PDF with mead m' and standard deviation \sigma'.

Homework Equations

The Attempt at a Solution

I really do not know where to go from here, i need a heads-up.
Thanks

 

[statdad]

Is aX + b to have a different mean but same standard deviation? I'm not entirely clear from your post.

You do know that if X is Gaussian then aX + b is also Guassian for any choices of a \ne 0 \text{ and real }b, right, so you don't need to show that part.

If \mu_1 is supposed to be the new mean, then

<br /> E(aX+b) = aE(X) + b = \mu_1<br />

The other condition requires you to work with the variances: If the standard deviation doesn't change then you know that

<br /> Var(aX+b) = \sigma^2<br />

Simplifying and working with these equations will let you find appropriate values for a, b. Play with them.

 

[ahamdiheme]

no the new deviation is \sigma&#039;

 

[statdad]

I'm not sure what you mean by saying "the new standard deviation is \sigma&#039;

Is it simply that

<br /> \sigma&#039; = \sqrt{Var(aX+b)}<br />

 

[ahamdiheme]

y=aX+b has a Gaussian PDF with mean m' and standard deviation '

that relationship, i know. the m' goes with \sigma&#039;.
Hope u understand what the question says now. It seems a little confusing but that's the exact way the textbook put it. Thank you