Project ForgeEngineering Mathematics
Calculus
GATE 2020
Medium
Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z=X+Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is __________ (round off to 2 decimal places).
-0.99(± 0.02 accepted)
Explanation
For exponential distributions with mean 0.5, Var(X)=Var(Y)=0.5²=0.25. Var(Z)=Var(X)+Var(Y)+2r√(Var(X)Var(Y)) = 0.25+0.25+2r(0.25) = 0.5+0.5r. Setting Var(Z)=0 gives r=−1.
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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