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
Q6: Suppose that X has a Weibull distribution with β=2 and δ=8.6. a. Find the mean...
2- 5. The Weibull distribution has many applications in reliability engineering, survival analysis, and general insurance. Let B>0, 8>0. Consider the probability density function x>0 zero otherwise Recall (Homework #1) V-Χδ has an Exponential(8-T )-Gamma(u-l,e-1 ) distribution. Let X1, . , X/ be a random sample from the above probability distribution. y-ΣΧ.Σν i has a Gamma(u-n, θ- 1 ) distribution. !!! i-l 2. suppose δ is known. Let Xi, X2, , Xn be a random sample from the distribution with...
Suppose that X has a Weibull distribution with B = 0.5 and 8 = 100 hours. Determine the following. Round the answers to 3 decimal places. (a) P(X < 10000) = (b) P(X > 5000) =
Suppose that the lifetime of a component (in hours), X, is modeled with a Weibull distribution with B 0.5 and = 3400. Determine the following in parts (a) and (b) Round your answers to three decimal places (e.g. 98.765) a) P(X> 3500) = i b) P(X> 6000|X > 3000) i c) Suppose that X has an exponential distribution with mean equal to 3400. Determine the following probability Round your answer to three decimal places (e.g. 98.765) P(X 6000X > 3000)...
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...
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...
The lifetime of a product can be modeled with a Weibull distribution with δ = 22 and β = 3. a. What is the expected lifetime of the product? b. What is the standard deviation of the product? c. The product costs $15,543 dollars to produce, but is expected to save $1,115 in costs for each year that it functions as advertised. Considering the initial cost, what is the expected savings in costs for this product? d. What is the...
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.
Suppose a distribution has a weibull distribution where lamda(t)= 3t^2. Find w such P(W>=w) = 1/e^8.
Suppose that the random variable X has a Weibull distribution with parameters a = 2.98 and λ = 0.23. Find P(3 ≤ X ≤ 7). Round your answer to the nearest ten thousandth.
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.)