Let Z ¼ N(0, 1), and let X = Ï Z + μ where μ and Ï > 0 are constants. Let represent the cumulative

Let Z ˆ¼ N(0, 1), and let X = σ Z + μ where μ and σ > 0 are constants. Let represent the cumulative distribution function of Z, and let φ represent the probability density function, so 

a. Show that the cumulative distribution function of

b. Differentiate F_X (x) to show that X ˆ¼ N(μ, σ²).

c. Now let X = ˆ’σ Z + μ. Compute the cumulative distribution function of X in terms of Φ, then differentiate it to show that X ˆ¼ N(μ, σ²).

|$(x) = (1//27)e?2 X is Fx(x) = O