Use the convolution formula, Theorem 6.9, to obtain the density of (X+Y) when (X) and (Y) are
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Use the convolution formula, Theorem 6.9, to obtain the density of \(X+Y\) when \(X\) and \(Y\) are independent and each has the exponential distribution with \(\beta=1\).
Data From Theorem 6.9
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Theorem 6.9 Let X and Y be independent and let X have density fx(x) and Y have density fy (y). Then the density of Z = X + Y is given by the convolution formula fx+y(z) = fx(x)fy(z - x) dx for all z The ratio of random variables Z = Y/X has density |x| fy/x(z) = | | x | x(x)fy(xz) dx for all z
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Related Book For
Probability And Statistics For Engineers
ISBN: 9780134435688
9th Global Edition
Authors: Richard Johnson, Irwin Miller, John Freund
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