For a continuous random variable x and constant a, P(x a) = P(x a) and P(x a) = P(x

Question

For a continuous random variable x and constant a, P(x  a) = P(x >a) and P(x  a) = P(x < a).

Quizplus · Accepted Answer

This is true because P(x > a) is the same as saying the probability that x is greater than a, and P(x < a) is the same as saying the probability that x is less than a. If we switch the inequality, we are essentially saying the same thing but with the complementary event (i.e. the probability that x is not greater than a, which is the same as the probability that x is less than or equal to a; and the probability that x is not less than a, which is the same as the probability that x is greater than or equal to a). Therefore, P(x > a) = P(x not less than or equal to a) = P(x >= a), and P(x < a) = P(x not greater than or equal to a) = P(x <= a).

For a Continuous Random Variable X and Constant A, P(x