4 10 pts. Let X1 X2 be a random sample from the exponential distribution with parameter θ What is the mgf of Y = X1 + X2? a) (4 pts.+) Find E(Y-E(X1 + X2] using the mgf. For 2 more points on test 2:...

Question

Question

4 10 pts. Let X1 X2 be a random sample from the exponential distribution with parameter θ What is the mgf of Y = X1 + X2? a)

Answer 1

Answer #1

Hence+ -unique nesl tharem

Answer 2

Similar Homework Help Questions

I. Let X be a random sample from an exponential distribution with unknown rate parameter θ...

I. Let X be a random sample from an exponential distribution with unknown rate parameter θ and p.d.f (a) Find the probability of X> 2. (b) Find the moment generating function of X, its mean and variance. (c) Show that if X1 and X2 are two independent random variables with exponential distribution with rate parameter θ, then Y = X1 + 2 is a random variable with a gamma distribution and determine its parameters (you can use the moment generating...
Let X1,X2,X3,X4 be observations of a random sample of n-4 from the exponential distribution having mean...

Let X1,X2,X3,X4 be observations of a random sample of n-4 from the exponential distribution having mean 5, What is the mgf of Y-X1 X2 X3 X4? 4. 5. What is the distribution of Y? What is the mgf of the sample mean X = X+X+Xa+X1 ? 6. 7. What is the distribution of the sample mean?
4. Let X1, X2, ..., Xn be a random sample from an Exponential(1) distribution. (a) Find...

4. Let X1, X2, ..., Xn be a random sample from an Exponential(1) distribution. (a) Find the pdf of the kth order statistic, Y = X(k). (b) Determine the distribution of U = e-Y.

Let X1, X2, ... , Xn be a random sample of size n from the exponential...

Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = (1/θ)e^(−x/θ) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ. Let X1, X2, ... , Xn be a random sample of size n from the exponential distribution whose pdf is f(x; θ) = θe^(−θx) , 0 < x < ∞, 0 <θ< ∞. Find the MVUE for θ.
5. (4 marks) Let X1, X2, ..., X, be a random sample from an exponential distribution...

5. (4 marks) Let X1, X2, ..., X, be a random sample from an exponential distribution with parameter A. Then it is known that E(X) = = Also, 21 i X has a chi-squared distribution with 2n degrees of freedom. Suppose that the time to failure of a component is exponentially distributed. The seven independent components have the failure times: 81, 16, 5, 11, 52, 90, 23 Using these observations, test whether the true average lifetime (u) is less than...
Let X1, X2, ..., Xr be independent exponential random variables with parameter λ. a. Find the...

Let X1, X2, ..., Xr be independent exponential random variables with parameter λ. a. Find the moment-generating function of Y = X1 + X2 + ... + Xr. b. What is the distribution of the random variable Y?

4. Let X1, X2, ..., Xn be a random sample from a distribution with the probability...

4. Let X1, X2, ..., Xn be a random sample from a distribution with the probability density function f(x; θ) = (1/2)e-11-01, o < x < oo,-oo < θ < oo. Find the NILE θ.
4. Let X1, X2, ..., Xn be a random sample from a distribution with the probability...

4. Let X1, X2, ..., Xn be a random sample from a distribution with the probability density function f(x; θ) = (1/2)e-11-01, o < x < oo,-oo < θ < oo. Find the NILE θ.
7. Suppose X1, X2, ..., Xn is a random sample from an exponential distribution with parameter...

7. Suppose X1, X2, ..., Xn is a random sample from an exponential distribution with parameter K. (Remember f(x;2) = 2e-Ax is the pdf for the exponential dist”.) a) Find the likelihood function, L(X1, X2, ..., Xn). b) Find the log-likelihood function, b = log L. c) Find dl/d, set the result = 0 and solve for 2.

7. (15 pts) Suppose X1, X2, ..., X, is a random sample from an exponential distribution...

7. (15 pts) Suppose X1, X2, ..., X, is a random sample from an exponential distribution with parameter 2. (Remember f(x;2) = ne-^x is the pdf for the exponential dista.) a) Find the likelihood function, L(X1, X2, Xn). b) Find the log-likelihood function, I = log L. c) Find d //d, set the result = 0 and solve for 2.