Question

The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint:...

The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint: start with confidence interval for μ)

f(x)=αβX^(β-1) exp(-αX^β)

a. Derive 92% large sample confidence interval for α.

b. Find maximum likelihood estimator of α.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint:...
The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint: start with confidence interval for μ) f(x)=αβXβ-1 exp(-αXβ) a.      Derive 92% large sample confidence interval for α. b.      Find maximum likelihood estimator of α.
The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint:...
The lifespan of a system component follows a Weibull distribution with α (unknown) and β=1. (hint: start with confidence interval for μ) f(x)=αβXβ-1 exp(-αXβ) a.      Derive 92% large sample confidence interval for α. b.      Find maximum likelihood estimator of α.
Assume that the lifespan of an Asian hornet follows a Weibull distribution with parameters β =...
Assume that the lifespan of an Asian hornet follows a Weibull distribution with parameters β = 2.0 and δ = 62 days. a)Determine the probability that an Asian hornet lives longer than 50 days. b)Determine the mean time in days until death of an Asian hornet. c)Determine the median life time of Asian hornet in days. (Hint: For median, m , P ( X ≤ m ) = 0.5 , X i s t h e l i f e...
The random variable X is uniformly distributed in the interval [0, α] for some α >...
The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α. (a) Derive the cumulative distribution function of Y . (b)...
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α]...
Included all steps. Thanks The random variable X is uniformly distributed in the interval [0, α] for some α > 0. Parameter α is fixed but unknown. In order to estimate α, a random sample X1, X2, . . . , Xn of independent and identically distributed random variables with the same distribution as X is collected, and the maximum value Y = max{X1, X2, ..., Xn} is considered as an estimator of α. (a) Derive the cumulative distribution function...
1. To estimate the mean of a population with unknown distribution shape and unknown standard deviation,...
1. To estimate the mean of a population with unknown distribution shape and unknown standard deviation, we take a random sample of size 64. The sample mean is 22.3 and the sample standard deviation is 8.8. If we wish to compute a 92% confidence interval for the population mean, what will be the t multiplier? (Hint: Use either a Probability Distribution Graph or the Calculator from Minitab.)
Let X ∼ Beta(α, β). (a) Show that EX 2 = (α + 1)α (α +...
Let X ∼ Beta(α, β). (a) Show that EX 2 = (α + 1)α (α + β + 1)(α + β) . (b) Use the fact that EX = α/(α + β) and your answer to the previous part to show that Var X = αβ (α + β) 2 (α + β + 1). (c) Suppose X is the proportion of free-throws made over the lifetime of a randomly sampled kid, and assume that X ∼ Beta(2, 8) ....
The water quality of a river was investigated by taking 15 water samples and recording the...
The water quality of a river was investigated by taking 15 water samples and recording the counts of a particular bacteria for each sample, where ???? is the number of bacteria in sample ?? and the ????’s are assumed to be independent and follow a Poisson ( ?oi(?) ) distribution. The data are as follows: {27, 24, 25, 21, 30, 22, 20, 22, 29, 19, 19, 22, 23, 36, 19} 1. Find a point estimate for the population mean number...
Suppose a random sample of size n was drawn from a distribution with pdf f(y,a)=(1/a )...
Suppose a random sample of size n was drawn from a distribution with pdf f(y,a)=(1/a ) exp(-y/a) where y is between y>0 and a>0. Write down the central limit theorem for the standardized sample mean in terms of a and find a formula for a 95% confidence interval ..(hint: this is the exponential distribution with mean a)
Question 1 A researcher wishes to find a 90% confidence interval estimate for an unknown population...
Question 1 A researcher wishes to find a 90% confidence interval estimate for an unknown population mean using a sample of size 25. The population standard deviation is 7.2. The confidence factor z α 2for this est Group of answer choices 1.28 1.645 1.96 Question 2 A 90% confidence interval estimate for an unknown population mean μ is (25.81, 29.51). The length of this CI estimate is Group of answer choices 1.96 1.85 3.7 1.645 Question 3 Data below refers...