Prove these 2 formulas of the weibull distribution
Part 1: Derive the expected value and find the asymptotic distribution. Part 2: Find the consistent estimator and use the central limit theorem b. Derive the expected value of X for the Weibull(X,2) distribution. c. Suppose X,.. .X,~iid Uniffo,0). Find the asymptotic distribution of Z-n(-Xm) max Let X, X, ~İ.id. Exp(β). a. Find a consistent estimator for the second moment E(X"). Use the mgf of X to prove that your estimator is consistent in the case β=2 b. Use the...
Prove the variance of Weibull Distribution. α^2Γ(2+1/β)-α^2Γ(1+1/β)^2
Prove the theorem THEOREM 12.8 Formulas for Curvature If Cis a smooth curve given by r(t), then the curvature K of Cattis TO) |rt) xr" K ro |r'OP
Prove that the plot of log(-log(S(t)) versus log(t) for data from Weibull distribution with pa- rameters ρ and γ gives approximately a straight line with slope γ and log(t) intercept log(p)/7
The Weibull distribution was introduced in Sect. 3.5. (a) Find the inverse cdf for the Weibull distribution. (b) Write a program to simulate n values from a Weibull distribution. Your program should have three inputs: the desired number of simulated values n and the two parameters α and β. It should have a single output: an n x 1 vector of simulated values. (c) Use your program from part (b) to simulate 10,000 values from a Weibull(4, 6) distribution and...
4. Show the PDF and CDF of two-parameters of Weibull distribution (1) Use MATLAB to plot three Weibull PDFS with the parameters (a) 7 = 100,B = 1.25 ; (b) 100, B 4 and (c) 10,B 1.25 (2) For the Weibull distribution with the distribution parameter 7 = 20, B =1.5, calculate its = mean and standard deviation (3) For the Weibull distribution with the distribution parameter ) = 20, B =1.5, calculate the probabilities: PCX<80), PCX<40), P(10<X<90) 4. Show...
For the Weibull distribution with parameters a and ), recall that for t > 0 the density function and distribution function are, respectively, f(t) = alºja-1e-(At)a F(t) = 1-e-(at)a Suppose that T has the Weibull distribution with parameters a = 1/2 and 1=9. (a) (4 points) Compute exactly P(1 < T < 1.01|T > 1). Show your work. Write your answer to 6 decimal places.
Let T,Tn be independent random variables with Weibull distributions with scale parameters ρι, . . . ,Pn and common shape γ. Prove that T min (T, . . . ,Tn) also has a Weibull distribution with shape y. Derive the distribution of T- min(Ti,...,Tn). man11
For the Weibull distribution with parameters a and \, recall that for t > 0 the density function and distribution function are, respectively, f(t) = alºja-1e-(At)a F(t) =1-e-(At)a Suppose that T has the Weibull distribution with parameters a = 1/2 and 1 = 9. an (4 points) Compute work. approximation of P(1 < T < 1.01 T > 1) using the hazard rate. Show y
Assume that the life (X) of an airbag system follows a Weibull distribution with B=0.5 and the mean life (p) is 200 months. Weibull Distribution (pdf): 2 f(2) B 8 -G for r20 (a) What is the probability that an airbag system lasts at least 200 months? (b) What is the probability that an airbag system fails between 120 months and 150 months?