Weibull distribution

10.2 Weibull distribution The exponential distribution and Rayleigh distributions are particular cases of the Weibull distribution. The Weibull distribution is genereally used to estimate the average life of materials. Its probability density function is given by: 8-1 fx (x) = if x 2 0 (4) = 0 elsewhere 1. Verify that the corresponding cumulative distribution function is equal to : Fx(x) = 1 -e-(#)". 2. What type of distribution do we get if we set the parameters of the Weibull distribution to 3 = 1, n = 1/x? 3. Show that if X = n(-log(U))1/B with U a uniform random variable on the intervalle [0, 1], then X follows a Weibull distribution of parameters (3, n)