Question

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

Answer #1

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?

If X is an exponential random variable with parameter λ,
calculate the cumulative distribution function and the probability
density function of exp(X).

Derive the cdf for an exponential distribution with parameter
λ.

Compute the median of an Exp(λ) distribution.
Compute the median of a Par(1) distribution.

Given the exponential distribution f(x) = λe^(−λx), where λ >
0 is a parameter. Derive the moment generating function M(t).
Further, from this mgf, find expressions for E(X) and V ar(X).

Let X1, ..., Xn be a sample from an exponential population with
parameter λ.
(a) Find the maximum likelihood estimator for λ. (NOT PI
FUNCTION)
(b) Is the estimator unbiased?
(c) Is the estimator consistent?

suppose random variable X has an exponential distribution with
parameter lambda=4. Find the median of X.

Suppose that X|λ is an exponential random variable with
parameter λ and that λ|p is geometric with parameter p. Further
suppose that p is uniform between zero and one. Determine the pdf
for the random variable X and compute E(X).

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

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