For a continuous distribution,P(X $\le$ 100)= P(X

Name: For a continuous distribution,P(X $\le$ 100)= P(X < 100).
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Question

For a continuous distribution,P(X $\le$ 100)= P(X < 100).

Quizplus · Accepted Answer

For continuous distributions, the probability of X being exactly equal to a specific value (in this case, X being exactly equal to 100) is equal to 0. Therefore, the probability of X being less than or equal to 100 (i.e. P(X≤100)) is equal to the probability of X being strictly less than 100 (i.e. P(X<100)). Therefore, P(X≤100) = P(X<100), and the statement is true.

For a Continuous Distribution,P(X ≤\le≤ 100)= P(X < 100)

For a Continuous Distribution,P(X $\le$ 100)= P(X < 100)