GATE EE 2015 Set 1 — Question 11
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Engineering Mathematics → Probability → Expectation & Variance
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Question
A random variable has probability density function as given below:If the expected value , then is ___________.
Correct answer
0.25 to 0.25
Solution
1.Use the normalization property of PDF: .
(Equation 1).2.Use the expected value formula: .
(Equation 2).3.Solve the system of equations:
From (1), . Substitute into (2):.
Then .
So, for .
4.Calculate :
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