GATE CE 2017 Set 1 — Question 26
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Engineering Mathematics → Probability → PMF, PDF & CDF
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Question
For the function , to be a valid probability density function, which one of the following statements is correct?
Correct answer
(B) a = 0.5, b = 1
Solution
For a function to be a valid probability density function (PDF) over the interval :
Checking the options:
(A)
(B) . Also, is always positive for .
(C)
(D) Thus, option (B) is the only correct statement.
1.
2. for all
Evaluating the integral:Checking the options:
(A)
(B) . Also, is always positive for .
(C)
(D) Thus, option (B) is the only correct statement.
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