Suppose that x is a continuous random variable with pdf fx a

Suppose that x is a continuous random variable with pdf, f(x), and CDF, F(x). Let x₁ and x₂ be numerical values in the range of x.

P(x₁ <=X<= x₂ )=Fx₂ - Fx₁. True or False?

Solution

The cdf means that if we differentiate it we get the pdf. So in this case the probability of a range is simple the F of the end points. So if we have P(x1<=X<=x2) = F(x2) - F(x1) which basically gives the area under the curve between these points. This statement is thus True.