Question

7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1...

7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1 and θ2, use the distribution function technique to find the probability density of Y=X1+X2 when
a) θ1 ≠ θ2
b) θ1 = θ2


7.7) With reference to the two random variables of Exercise 7.5, show that if θ1 = θ2 = 1, the random variable Z1=X1/(X1 + X2) has the uniform density with α=0 and β=1.
                                     (I ONLY NEED TO ANSWER 7.7)

Homework Answers

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
7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1...
7.5) If X1 and X2 are independent random variables having exponential densities with the parameters θ1 and θ2, use the distribution function technique to find the probability density of Y=X1+X2 when a) θ1 ≠ θ2 b) θ1 = θ2 7.7) With reference to the two random variables of Exercise 7.5, show that if θ1 = θ2 = 1, the random variable Z1=X1/(X1 + X2) has the uniform density with α=0 and β=1.                                      (I ONLY NEED TO ANSWER 7.7)
If X1 and X2 are independent exponential random variables with respective parameters 1 and 2, find...
If X1 and X2 are independent exponential random variables with respective parameters 1 and 2, find the distribution of Z = min{X1, X2}.
If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find...
If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find the distribution of Z = min{X1, X2}.
Let X1 and X2 be two independent random variables having gamma distribution with parameters α1 =...
Let X1 and X2 be two independent random variables having gamma distribution with parameters α1 = 3, β1 = 3 and α2 = 5, β2 = 1, respectively. We are interested in finding the distribution of Y = 2X1 + 6X2. A standard approach is to apply a two-step procedure as that in question 2. However, as we discussed in the class, if the MGF technique is applicable, then it would be preferred due to its simplicity. (a) Find the...
Let X1 and X2 be independent Poisson random variables with respective parameters λ1 and λ2. Find...
Let X1 and X2 be independent Poisson random variables with respective parameters λ1 and λ2. Find the conditional probability mass function P(X1 = k | X1 + X2 = n).
Let X1,X2,..., Xn be independent random variables that are exponentially distributed with respective parameters λ1,λ2,..., λn....
Let X1,X2,..., Xn be independent random variables that are exponentially distributed with respective parameters λ1,λ2,..., λn. Identify the distribution of the minimum V = min{X1,X2,...,Xn}.
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1).
Let X1, X2, . . . Xn be iid exponential random variables with unknown mean β....
Let X1, X2, . . . Xn be iid exponential random variables with unknown mean β. Find the method of moments estimator of β
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y )
Let X1 and X2 be independent random variables such that X1 ∼ P oisson(λ1) and X2...
Let X1 and X2 be independent random variables such that X1 ∼ P oisson(λ1) and X2 ∼ P oisson(λ2). Find the distribution of Y = X1 + X2.s
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT