Question

Let X be an exponential random variable. Suppose E[X|X>a]=b, where b>a>0 are two constants. Compute the...

Let X be an exponential random variable. Suppose E[X|X>a]=b, where b>a>0 are two constants. Compute the probability P(X>a|X>a).

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Solution for probability P(X>b|X>a)

Let parameter of given exponential distribution is . From the given pdf we have

The conditional pdf is:

Now,

  

Since so

--------------------

So,

Putting   gives:


thank you for asking...

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that X is an exponential random variable with pdf f(x) = e^(-x),0<x<∞, and zero otherwise....
Suppose that X is an exponential random variable with pdf f(x) = e^(-x),0<x<∞, and zero otherwise. a. compute the exact probability that X takes on a value more than two standard deviations away from its mean. b. use chebychev's inequality to find a bound on this probability
a) Suppose that X is a uniform continuous random variable where 0 < x < 5....
a) Suppose that X is a uniform continuous random variable where 0 < x < 5. Find the pdf f(x) and use it to find P(2 < x < 3.5). b) Suppose that Y has an exponential distribution with mean 20. Find the pdf f(y) and use it to compute P(18 < Y < 23). c) Let X be a beta random variable a = 2 and b = 3. Find P(0.25 < X < 0.50)
Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and...
Let random variable X ∼ U(0, 1). Let Y = a + bX, where a and b are constants. (a) Find the distribution of Y . (b) Find the mean and variance of Y . (c) Find a and b so that Y ∼ U(−1, 1). (d) Explain how to find a function (transformation), r(), so that W = r(X) has an exponential distribution with pdf f(w) = e^ −w, w > 0.
Let X be a random variable with an exponential distribution and suppose P(X > 1.5) =...
Let X be a random variable with an exponential distribution and suppose P(X > 1.5) = .0123 What is the value of λ? What are the expected value and variance? What is P(X < 1)?
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) .
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).
Let t be a random value of a variable with exponential density e −t , t...
Let t be a random value of a variable with exponential density e −t , t > 0, and let Y be Poisson with parameter t. Find P(Y = 2). A. 1/4 B. 1/2 C. 1/8 D. 1/e
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...
1. Suppose a random variable X has a probability density function f(x)= {cx^2 -1<x<1, {0 otherwise...
1. Suppose a random variable X has a probability density function f(x)= {cx^2 -1<x<1, {0 otherwise where c > 0. (a) Determine c. (b) Find the cdf F (). (c) Compute P (-0.5 < X < 0.75). (d) Compute P (|X| > 0.25). (e) Compute P (X > 0.75 | X > 0). (f) Compute P (|X| > 0.75| |X| > 0.5).
Let X be a random variable with possible values {−2, 0, 2} and such that P(X...
Let X be a random variable with possible values {−2, 0, 2} and such that P(X = 0) = 0.2. Compute E(X^2 ).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT