Question

Compute and compare **λ(t)** for exponential,
Weibull distribution, and Gamma distribution.

Answer #1

Compute the quantile function of the exponential distribution
with parameter λ. Find its median (the 50th percentile).

Compute the quantile function of the exponential distribution
with parameter λ. Find its median (the 50th percentile).

Suppose that X is exponential with parameter λ. Compute the
median of X (i.e. the t for which P(X ≤ t) = 1/2). Is it smaller or
larger than the expectation?

A random variable XX with distribution
Exponential(λ)Exponential(λ) has the memory-less
property, i.e.,
P(X>r+t|X>r)=P(X>t) for all r≥0 and
t≥0.P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0.
A postal clerk spends with his or her customer has an
exponential distribution with a mean of 3 min3 min. Suppose a
customer has spent 2.5 min2.5 min with a postal clerk. What is the
probability that he or she will spend at least an additional 2 min2
min with the postal clerk?

Derive the cdf for an exponential distribution with parameter
λ.

when doing Anderson Darling test for Weibull distribution, how
to get gamma, beta, and alpha.
note :
I am using Excel.

For the hierarchical model Y |Λ ∼ Poisson(Λ) and Λ ∼ Gamma(α,
β), find the marginal distribution, mean, and variance of Y . Show
that the marginal distribution of Y is a negative binomial if α is
an integer. (b) Show that the three-stage model Y|N∼Binomial(N,p),
N|Λ∼Poisson(Λ), andΛ∼Gamma(α,β) leads to the same marginal
distribution of Y .

A particular circulation pump has a Weibull lifetime
distribution with a rate parameter λ = 0.064 per 1000 hours and a
shape parameter β = 1.23. What is the probability that this pump
will run for at least 1300 hours? Express your answer rounded to
three decimal places.

what is the log- likelihood function of the generalized gamma
distribution f(x; a,k,λ)?

Use Rstudio to compare the cdf and pdf of an exponential random
variable with rate λ=2λ=2 with the cdf and pdf of an exponential
random variable with rate 1/2.

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