Which value does the total integral of a density function over its domain equal?

Which value does the total integral of a density function over its domain equal?

• A. 0
• B. 1
• C. The total integral over the domain equals 1
• D. The area under the entire curve is undefined

Answer: (C)

For a probability density function, the integral across all possible values represents total probability. That total must be 1, because the variable will take some value in its domain with probability 1. So the integral over the entire domain equals 1, and the area under the curve on any subinterval gives the probability of the variable falling in that subinterval. If a density didn’t integrate to 1, it wouldn’t be a valid density.

For a probability density function, the integral across all possible values represents total probability. That total must be 1, because the variable will take some value in its domain with probability 1. So the integral over the entire domain equals 1, and the area under the curve on any subinterval gives the probability of the variable falling in that subinterval. If a density didn’t integrate to 1, it wouldn’t be a valid density.