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Gaussian PDF

  1. Nov 1, 2008 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    3. The attempt at a solution
    I really do not know where to go from here, i need a heads-up.
  2. jcsd
  3. Nov 1, 2008 #2


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    Homework Helper

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

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

    If [tex] \mu_1 [/tex] is supposed to be the new mean, then

    E(aX+b) = aE(X) + b = \mu_1

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

    Var(aX+b) = \sigma^2

    Simplifying and working with these equations will let you find appropriate values for [tex] a, b [/tex]. Play with them.
  4. Nov 3, 2008 #3
    no the new deviation is [tex]\sigma'[/tex]
  5. Nov 3, 2008 #4


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    Homework Helper

    I'm not sure what you mean by saying "the new standard deviation is [tex] \sigma' [/tex]

    Is it simply that

    \sigma' = \sqrt{Var(aX+b)}
  6. Nov 3, 2008 #5
    that relationship, i know. the m' goes with [tex]\sigma'[/tex].
    Hope u understand what the question says now. It seems a little confusing but thats the exact way the textbook put it. Thank you
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