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

Name: For any random variable x and constant a, P(x a) = P(x < a) because P(x = a) = 0.
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Question

For any random variable x and constant a, P(x  a) = P(x < a) because P(x = a) = 0.

Quizplus · Accepted Answer

The statement is false. P(x < a) and P(x ≤ a) are equivalent statements, not P(x < a) and P(x = a). If x is a continuous random variable, then P(x = a) is actually equal to 0. However, if x is a discrete random variable, P(x = a) may not necessarily be equal to 0.

For Any Random Variable X and Constant A, P(x