Question

Problem #3. X is a random variable with an exponential distribution with rate λ = 7...

Problem #3. X is a random variable with an exponential distribution with rate λ = 7 Thus the pdf of X is f(x) = λ e−λx

for 0 ≤ x where λ = 7.

PLEASE ANSWER these parts if you can.

f) Calculate the probability that X is at least .3 more than its expected value.Use the pexp function:

g) Copy your R script for the above into the text box here.

Homework Answers

Answer #1

TOPIC:Exponential distribution and probability.

Required R code and output:

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Problem #3. X is a random variable with an exponential distribution with rate λ = 7...
Problem #3. X is a random variable with an exponential distribution with rate λ = 7 Thus the pdf of X is f(x) = λ e−λx for 0 ≤ x where λ = 7. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the f(x) above and the R integrate function calculate the expected value of X2 c) Using the dexp function and the R integrate command calculate the expected value...
If X is an exponential random variable with parameter λ, calculate the cumulative distribution function and...
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...
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).
Given the exponential distribution f(x) = λe^(−λx), where λ > 0 is a parameter. Derive the...
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).
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...
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?
Question 7) Suppose X is a Normal random variable with with expected value 31 and standard...
Question 7) Suppose X is a Normal random variable with with expected value 31 and standard deviation 3.11. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X>32.1): b) Find the probability P(X >32.1) when n = 4: c) Find the probability P(X >32.1) when n = 25: d) What is the probability P(31.8 <X <32.5) when n = 25?...
Question 6) Suppose X is a random variable taking on possible values 0,2,4 with respective probabilities...
Question 6) Suppose X is a random variable taking on possible values 0,2,4 with respective probabilities .5, .3, and .2. Y is a random variable independent from X taking on possible values 1,3,5 with respective probabilities .2, .2, and .6. Use R to determine the following. f) Find the expected value of X*Y. (i.e. X times Y) g) Find the expected value of 3X - 5Y. h) Find the variance of 3X - 5Y i) Find the expected value of...
Use Rstudio to compare the cdf and pdf of an exponential random variable with rate λ=2λ=2...
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.
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤...
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤ x < ∞ 0 otherwise } for some λ > 0. a. Compute the cumulative distribution function F(x), where F(x) = Prob(X < x) viewed as a function of x. b. The α-percentile of a random variable is the number mα such that F(mα) = α, where α ∈ (0, 1). Compute the α-percentile of the random variable X. The value of mα will...
Let X be an exponential random variable with parameter λ > 0. Find the probabilities P(...
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) .