Question

A probability density function f(x) for the continuous random variable X is denoted as _______

(a) ∫ f(x)dx = ∞, -1<=x<=1

(b) ∫ f(x)dx = 1, -∞<=x<=∞

(c) ∫ f(x)dx = 0, -∞<=x<=∞

(d) ∫ f(x+2)dx = .5, -∞<=x<=∞

I got this question in quiz.

I'd like to ask this question from Discrete Probability in division Discrete Probability of Discrete Mathematics

Answer 1

The correct choice is (b) ∫ f(x)dx = 1, -∞<=x<=∞

The explanation: A probability density function f(x) for the continuous random variable X is denoted as ∫ f(x)dx = 1, -∞<=x<=∞. The area under the curve between any two ordinates x = a and x = b is a probability that X lies between a and b. So, ∫f(x)dx = P(a≤X≤b).