Prove the variance of Weibull Distribution.
α^2Γ(2+1/β)-α^2Γ(1+1/β)^2
Solution-:
Prove the variance of Weibull Distribution. α^2Γ(2+1/β)-α^2Γ(1+1/β)^2
The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β = 3. Compute the following.
The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β = 3.Compute the following. (Round your answers to three decimal places.)
Q6: Suppose that X has a Weibull distribution with β=2 and δ=8.6. a. Find the mean and the variance b. Determine the following: (a) P(X< 10) (b) P (X> 9) (c) P (8<x<11) (d) Value for x such that P(X>x) = 0.9
Prove these 2 formulas of the weibull distribution THEOREM THEOREM
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...
with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a) Suppose that α 4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β. (Hint: What is E(Y)?) (b) Suppose that β 4 is known and α is unknown. Find a complete sufficient statistic for a. with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a)...
Let X1 ,……, Xn be a random sample from a Gamma(α,β) distribution, α> 0; β> 0. Show that T = (∑n i=1 Xi, ∏ n i=1 Xi) is complete and sufficient for (α, β).
The lifetime of a drill bit in a mechanical operation, in hours, has a Weibull distribution with α = 0.5 and β = 2.2. Calculate the probability that the bit will fail after 2.8 hours Answer using 4 decimals.
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...
Let α,β,γ denote words of length n; d(α,β) denotes the distance between the words α and β. Prove the following triangle inequality: d(α, γ) ≤ d(α, β) + d(β, γ)