Suppose X is a continuous random variable with f ( x ) f ( x ) on [ 1 , 5 ] [ 1 , 5 ] as the associated density function. P ( 1 < X < 5 ) P ( 1 < X < 5 ) =

Answer 1

As X is a continuous r.v. defined on [1,5], P(1) = P(5) = 0 (a continuous r.v. has 0 probability of being at any particular point), so

P(1 < X < 5) = P(1 <= X <= 5) - P(X = 1) - P(X = 5) = 1 - 0 - 0 = 1