IGNOU MTE 3 2026 - For , find the E(x) and V(x).

Question

For $f(x) = \theta e^{-\theta x}, x \geq 0, \theta > 0$ , find the E(x) and V(x).

09 Jan 2026

Answer :

Word Count : 214

For the probability density function (f(x) = \theta e^{-\theta x}), (x \ge 0), (\theta > 0), we calculate the expected value (E(X)) and variance (V(X)) manually. Step 1: Expected value (E(X)) [ E(X) = \int_0^\infty x f(x) , dx = \int_0^\infty x \theta e^{-\theta x} , dx ] Use integration by parts: let (u = x \implies du = dx), (dv = \theta e^{-\theta x} dx

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