Let X be a continuous random variable with probability densi

Let X be a continuous random variable with probability density function f(x) and cumulative distribution function F(x). Then for any two numbers, a and b where a < b, which of the following is true?

a) F(x) = (x-a)/(b-a)

b) P(X > a) = 1 - F(a)

c) P(X > b) = F(b) - 1

d) P(a <= X <= b) = F(a) - F(b)

Solution

a) is not true outside the range of (a,b)

b) is true,

c) is false, should be 1 - F(b)

d) should be F(b) - F(a)