Let Z ~ N(0,1), and let X = ?Z + µwhere µand ?> 0 are constants. Let ? represent the cumulative distribution function of Z, and let ? represent the probability density function, so 
.
a. Show that the cumulative distribution function of X is 
b. Differentiate 
to show that 
c. Now let X = ??Z+ µ.Compute the cumulative distribution function of X in terms of?, then differentiate it to show that 
.
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