For any continuous random variable X, if both a and b are fixed real numbers such that a

Question

For any continuous random variable X, if both a and b are fixed real numbers such that a < b, then P(a ≤ X ≤ b) will always be:
A) P(X < b).
B) P(X ≤ b).
C) P(X ≤ b) - P(X < a)
D) Both A and B are correct.

Quizplus · Accepted Answer

P(a ≤ X ≤ b) can also be written as P(X ≤ b) - P(X < a) by the complement rule of probability. Therefore, the correct answer is C. A and B are incorrect because they do not take into account the possibility that X could be between a and b.

For Any Continuous Random Variable X, If Both a and B