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

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

For a continuous random variable x and constant a, P(x  a) = P(x > a) because P(x = a) = 0.

Quizplus · Accepted Answer

This is true. For a continuous random variable, the probability of any single value is zero, so P(x > a) is equivalent to P(x ≥ a). Similarly, P(x < a) is equivalent to P(x ≤ a). Therefore, P(x > a) = 1 - P(x ≤ a) = 1 - P(x < a) = P(x ≥ a).

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