Problem 15E

Let Y = X2.

(a) Find the pdf of Y when the distribution of X is N(0, 1).

(b) Find the pdf of Y when the pdf of X is f (x) = (3/2)x2, − 1 < x < 1.

Lecture 7: 8.5 General Continuous Random Variables Definition: - A curve (or function) is called a Probability Density Curve if: 1. It lies on or above the horizontal axis. 2. Total area under the curve is equal to 1. - KEY IDEA: AREA under a density curve over a range of values corresponds to the PROBABILITY that the random variable X takes on a value in that range. - The probability that the variable X exactly equals a specified value is 0. - Instead, we find the probability that X could take on values in an interval. 8.6 Normal Random Variables A Normal Curve: Symmetric, bell-‐shaped, centered