A continuous random variable X has uncountably many values in the interval [a, b] . If C is a value in the interval [a, b] , then P(X = C) is: - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live | ExamTest.live

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A continuous random variable X has uncountably many values in the interval [a, b] . If C is a value in the interval [a, b], then P (X = C) is:

A $is zero$
B $is strictly non-zero$
C $depends on the limits {a, b}$
D $is less than one, but non-zero$

Solution & Step-by-step Explanation

For any continuous random variable, the probability of the variable taking an exact single point value is always zero because the area under the density curve at a point is zero. P (X = c) = \int_{c}^{c} f (x) d x = 0

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A continuous random variable X has uncountably many values in the interval [a, b] . If C is a value in the interval [a, b], then P (X = C) is:

A

is zero

B

is strictly non-zero

C

depends on the limits {a, b}

D

is less than one, but non-zero

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Probability Continuous Random Variable

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