Question

Give the definition of *memoryless* for a random variable
*X*. (b) Show that if *X* is an exponential random
variable with parameter λ, then *X* is memoryless. (c) The
life of the brakes on a car is exponentially distributed with mean
50,000 miles. What is that probability that a car gets at least
70,000 miles from a set of brakes **if it already has 50,000
miles**?

Answer #1

A random variable X is exponentially distributed with
an expected value of 77
a-1. What is the rate parameter λ?
a-2. What is the standard deviation of
X?
b. Compute P(68 ≤ X ≤ 86)

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

The random variable X is exponentially distributed, where X
represents the waiting time to see a shooting star during a meteor
shower. If X has an average value of 71 seconds, what are the
parameters of the exponential distribution?
λ=71, μ=71, σ=171
λ=171, μ=71, σ=71
λ=71, μ=171, σ=171
λ=271, μ=71, σ=712
λ=712, μ=71, σ=171

1. Show that if X is a Poisson random variable with parameter
λ, then its variance is λ
2.Show that if X is a Binomial random variable with parameters
n and p, then the its variance is npq.

Let U be a Standard Uniform random variable. Show all the steps
required to generate:
An exponential random variable with the parameter λ = 3.0;
A Bernoulli random variable with the probability of success
0.65;
A Binomial random variable with parameters n = 12 and p =
0.6;

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).

A random variable X is exponentially distributed with a
mean of 0.16.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X?
(Round your answer to 2 decimal places.)
b. Compute P(X > 0.25).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
c. Compute P(0.14 ≤ X ≤ 0.25).
(Round intermediate calculations to at least 4 decimal
places and final...

A Poisson random variable is a variable X that takes on the
integer values 0 , 1 , 2 , … with a probability mass function given
by p ( i ) = P { X = i } = e − λ λ i i ! for i = 0 , 1 , 2 … ,
where the parameter λ > 0 .
A)Show that ∑ i p ( i ) = 1.
B) Show that the Poisson random...

Let X be an exponential random variable with parameter λ > 0.
Find the probabilities P( X > 2/ λ ) and P(| X − 1 /λ | < 2/
λ) .

A random variable X is exponentially distributed with an
expected value of 33.
a-1. What is the rate parameter λ? (Round your answer to 3
decimal places.)
a-2. What is the standard deviation of X?
b. Compute P(23 ≤ X ≤ 43). (Round intermediate calculations to
at least 4 decimal places and final answer to 4 decimal
places.)
c. Compute P(20 ≤ X ≤ 46). (Round intermediate calculations to
at least 4 decimal places and final answer to 4 decimal...

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