Suppose that two independent and identically distributed random variables X and Y have common mgf MX(t) = MY (t) = (e^t)/(1− t^2) . Find (a) E[X] (b) M(3X−7Y +5)(t).
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Suppose that two independent and identically distributed random variables X and Y have common mgf MX(t) = MY (t) = (e^t)/(1− t^2) . Find (a) E[X] (b) M(3X−7Y +5)(t).
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- If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).9. Let X and Y be independent exponentially distributed RVs with parameters A and B, respectively. Use the MGF approach to find the CDF and the PDF of Z = X+Y. E [e=²(*^_^₂)] = E [e³*] E[e³r] *M(s) XAY = M₁ (3) My (1) = (-_^) ( P-²) =A random process X(t) is applied as input to a system whose impulse response is h(t) 3u(t)t² exp (-8t). If E[X(t)] = 2, what is the mean value of the system response y(t). - CS Scanned with CamScanner
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