GATE ME 2020 Set 1 — Question 45
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Engineering Mathematics → Probability → Correlation & Covariance
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Question
Consider two exponentially distributed random variables and , both having a mean of 0.50. Let and be the correlation coefficient between and . If the variance of equals 0, then the value of is ________ (round off to 2 decimal places).
Correct answer
-1
Solution
The variance of the sum of two random variables is given by:We know that , where is the correlation coefficient.For an exponential distribution with mean , the variance is .
Given and :Given :The value of is .
Given and :Given :The value of is .
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