For every random variable, P(a ≤ x ≤ b) = P(a

Name: For every random variable, P(a ≤ x ≤ b) = P(a < x < b).
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Question

For every random variable, P(a ≤ x ≤ b) = P(a < x < b).

Quizplus · Accepted Answer

If the random variable is continuous, then P(a ≤ x ≤ b) = P(a < x < b) both evaluate to the same value. However, if the random variable is discrete, then P(a ≤ x ≤ b) includes the probability mass at a and/or b, but P(a < x < b) does not. Therefore, the two probabilities are not equal.

For Every Random Variable, P(a ≤ X ≤ B) =