Let X be N(0, 1). Find the pdf of Y =

Chapter 5, Problem 14E

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QUESTION:

Problem 14E

Let X be N(0, 1). Find the pdf of Y = |X|, a distribution that is often called the half-normal. Hint: Here y Sy = {y : 0 < y < ∞}. Consider the two transformations x1 = −y,−∞ < x1 < 0, and x2 = y, 0 < y < ∞.

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QUESTION:

Problem 14E

Let X be N(0, 1). Find the pdf of Y = |X|, a distribution that is often called the half-normal. Hint: Here y Sy = {y : 0 < y < ∞}. Consider the two transformations x1 = −y,−∞ < x1 < 0, and x2 = y, 0 < y < ∞.

ANSWER:

Step 1 of 4

Since X is, the p.d.f of X is:

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