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Converting Normal Distribution to Standard Normal

  1. Mar 6, 2014 #1
    1. The problem statement, all variables and given/known data

    Let X1,X2,X3 be a random sample from a normal distribution with mean μ≠0 and variance σ2=1/24. What are the values of a and b, respectively, in order for L=aX1+4X2+bX3 to have standard normal distribution?


    2. Relevant equations

    σ=1/√24

    Converting normal distribution to Standard Z=(X-μ)/σ




    3. The attempt at a solution

    I tried to set this up by calculating Z for each value of X and setting it equal to L

    aX1+4X2+bX3= (X1-μ)/(1/√24) + (X2-μ)/(1/√24) + (X3-μ)/(1/√24)

    But doesn't this just mean that a=b=4? I don't really know how to tackle this problem. Any help is appreciated!
     
  2. jcsd
  3. Mar 6, 2014 #2

    Ray Vickson

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    What are the mean and variance of L, in terms of 'a' and 'b'?
     
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