Let Z ¼ N(0, 1), and let X = Ï Z + μ where μ and Ï
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a. Show that the cumulative distribution function of
b. Differentiate FX (x) to show that X ¼ N(μ, Ï2).
c. Now let X = Ï Z + μ. Compute the cumulative distribution function of X in terms of Φ, then differentiate it to show that X ¼ N(μ, Ï2).
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