Let f(z) be the continuous probability density function of a random variable z. The probability that a

Question

Let f(z) be the continuous probability density function of a random variable z. The probability that a < z <= b is:

A. f(b) - f(a)
B. f(b - a)
C. integral_{a}^{b} f(z) dz
D. integral_{a}^{b} f(z) dz    [Note: same as C but asking about the role of f as a density]

Accepted Answer

C. integral_{a}^{b} f(z) dz For a continuous random variable, the probability that Z falls in an interval [a, b] is the area under the PDF curve between a and b. The PDF f(z) itself is not a probability; only the integral of f gives probability. The difference f(b)-f(a) would be meaningful for a CDF F, not a PDF f.

Let f(z) be the continuous probability density function of a random variable z. The probability that a < z <= b is: A. f(b) - f(a) B. f(b - a) C. integral_{a}^{b} f(z) dz D. integral_{a}^{b} f(z) dz [Note: same as C but asking about the role of f as a density]