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GATE DA 2024 Set 1 — Question 57

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NAT+2 / -0EasyExponentialContinuous Random VariablesProbability & StatisticsExpectation (Continuous)Variance (Continuous)

Probability & Statistics → Continuous Random Variables → Expectation (Continuous)

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Question

Let XX be a random variable exponentially distributed with parameter λ>0\lambda > 0. The probability density function of XX is given by:fX(x)={λe−λx,x≥00,otherwisef_X(x) = \begin{cases} \lambda e^{-\lambda x}, & x \geq 0 \\ 0, & otherwise \end{cases}If 5E(X)=Var(X)5E(X) = Var(X), where E(X) and Var(X)Var(X) indicate the expectation and variance of XX, respectively, the value of λ\lambda is ______ (rounded off to one decimal place).
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