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Let Y have an exponential distribution with mean ?. Prove that W=?y has a weibull density with ?= ? and m=2 Solution f(y,ß) = (1/ß)*e^(-y/ß) and F(y,ß) = 1-e^(-y/ß) W = vy = y^(0.5) now put y^0.5 in place of y in F(y,ß) we get = 1-e^{(-(y)/ß)^0.5} for weibull distribution , F( x,m,a) = 1-e^{[- (x/a)]^(1/m)} comparing to the above 1/m = 0.5 ; m =2 and a=ß.

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Let Y have an exponential distribution with mean ?. Prove that W=?y has a weibull density with ?= ? and m=2 Solution f(y,ß) = (1/ß)*e^(-y/ß) and F(y,ß) = 1-e^(-y/ß) W = vy = y^(0.5) now put y^0.5 in place of y in F(y,ß) we get = 1-e^{(-(y)/ß)^0.5} for weibull distribution , F( x,m,a) = 1-e^{[- (x/a)]^(1/m)} comparing to the above 1/m = 0.5 ; m =2 and a=ß

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Let Y have an exponential distribution with mean . Prove that W.pdf

  • 1. Let Y have an exponential distribution with mean ?. Prove that W=?y has a weibull density with ?= ? and m=2 Solution f(y,ß) = (1/ß)*e^(-y/ß) and F(y,ß) = 1-e^(-y/ß) W = vy = y^(0.5) now put y^0.5 in place of y in F(y,ß) we get = 1-e^{(-(y)/ß)^0.5} for weibull distribution , F( x,m,a) = 1-e^{[- (x/a)]^(1/m)} comparing to the above 1/m = 0.5 ; m =2 and a=ß