Question

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

Answer #1

Median of exponential distribution =

= ln(2) / 4

= 0.1733 (ans)

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

1. Suppose that X has an Exponential distribution with rate
parameter λ = 1/4. Also suppose that given X = x, Y has a
Uniform(x, x + 1) distribution.
(a) Sketch a plot representing the joint pdf of (X, Y ). Your
plot does not have to be exact, but it should clearly display the
main features. Be sure to label your axes.
(b) Find E(Y ).
(c) Find Var(Y ).
(d) What is the marginal pdf of Y ?

. X has exponential distribution with parameter 4. Therefore
E[X] = 1/4 .
Find P(X > 6) and P(X > 6|X > 1).
Find E[X|X > 1].
Would someone help me with the correct detail solutions to the
problems

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

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X, T are independent exponential random variables with
parameters Lambda(X) and Lambda(T). Find the conditional density of
X given X<T

Suppose that X is exponential with parameter λ. Compute the
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larger than the expectation?

Let X be an exponential random variable with parameter λ > 0.
Find the probabilities P( X > 2/ λ ) and P(| X − 1 /λ | < 2/
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Assume that X has an exponential distribution with parameter θ =
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A) Find P(X ≤ 1). Give your answer to 4 decimal
places
B) Find P(2 ≤ X ≤ 10). Give your answer to 4
decimal places.

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