GATE CE 2019 Set 2 — Question 36
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Engineering Mathematics → Probability → PMF, PDF & CDF
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Question
The probability density function of a continuous random variable distributed uniformly between and (for ) is
Correct answer
(B) (1)/(y-x)
Solution
For a continuous random variable distributed uniformly between and (where ), the probability density function (PDF) is given by:
In this question, the random variable is distributed uniformly between and , with the condition . Therefore, we can set and .Substituting these values into the PDF formula:
Comparing this with the given options, option (B) matches the derived PDF.Options (A) would be negative since , which is not possible for a PDF.
Options (C) and (D) are not in the form of a probability density function (which must integrate to 1 over its range).
In this question, the random variable is distributed uniformly between and , with the condition . Therefore, we can set and .Substituting these values into the PDF formula:
Comparing this with the given options, option (B) matches the derived PDF.Options (A) would be negative since , which is not possible for a PDF.
Options (C) and (D) are not in the form of a probability density function (which must integrate to 1 over its range).
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