Question
In: Statistics and Probability
The lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose...
The lifespan of an electrical component has an exponential
distribution with parameter lambda = 0.013. Suppose we have an iid
sample of size 100 of these components
Some hints: P(X < c) for an exponential(lambda) can be found via
pexp(c,lambda) E[X] = 1/lambda and Var[X] = 1/lambda^2
Round all answers to 4 decimals
Using the exact probability distribution, what is the probability
that a single component will be within 15.38 units of the
population mean?
Using Chebyshev's inequality, what is a lower bound on the probability that the sample mean will be within 15.38 units of the population mean?
Using the CLT, what is an approximation to the probability that the sample mean will be within 15.38 units of the population mean?
Solutions
orchestra answered 1 year agoRelated Solutions
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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:
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f(x)=αβXβ-1 exp(-αXβ)
a. Derive
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b. Find the
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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:
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a. Derive
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likelihood estimator of α.
The lifespan of a system component follows a Gamma distribution with β (unknown) and α=1. (hint:...
The lifespan of a system component follows a Gamma distribution
with β (unknown) and α=1. (hint: start with
confidence interval for μ)
f(x)=(1/βα Γ(α)) Xα-1 e-X/β
a. Derive
98% large sample confidence interval for β.
b. Find maximum
likelihood estimator of β.
a) 98% large sample confidence interval fo β is
b) MLE for β is
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