ZuoTi.Pro
Question

You are given that a random variable, N, has the geometric distribution, 3-1 PIN = n] = _ for n=1, 2, ,. Random variables, 偶; j=1, 2, . ) do not depend on N and are independent with the common exponential distribution, with the mean equal to θ 2, or equivalently (2)-, e-0.5x, for x 〉 0. Consider a random sum, 1. Derive the marginal expectation of S 2. Derive the marginal variance of S. 3. Find the marginal second moment of S, that is E [S2

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

J, 27 , m, where h 0.5 2 0 O.W. e. 2 0 U.w. Var (x): θ2-22-4. We know that if X~ExponenhaLl®)Th e m ainal expectahin of S is Nowd i-1 As xjs ave independent 2n E(S/N) 2N Now/ E (S)E ESN) E 2 N2 The inal vamiance of S is Vavt s) ow 3-1 ave inde pendent j- itj i + 一4m.No w Var (s) /于 4x12 + 4x4 64 al Se marginal second moment of is 2 61 8 2 8

0 0
Add a comment
Know the answer?
Add Answer to:
You are given that a random variable, N, has the geometric distribution, 3-1 PIN = n]...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • Problem 7: 10 points Consider independent random variables, [Y: 1, 2, ..., ), having the same...

    Problem 7: 10 points Consider independent random variables, [Y: 1, 2, ..., ), having the same Gamma distribution, with the density, .узе-2y for y > 0 Suppose that a random variable, N, does not depend on all Y, and is geometrically distributed, so that PIN = n] = n, for n=1, 2, Consider a random sum, S Y 1. Determine the marginal expectation of S. 2. Determine the marginal variance of S.

  • Problem 10: 10 points Assume that a random variable (L) follows the exponential distribution with intensity...

    Problem 10: 10 points Assume that a random variable (L) follows the exponential distribution with intensity λ-1. Given L-u, a random variable Y has the Poisson distribution with parameter - u. 1. Derive the marginal distribution of Y and evaluate probabilities, PY=n] , for n = 0,1,2, 2. Find the expectation of Y, that is E Y 3. Find the variance of Y, that is Var Y

  • A discrete random variable has the distribution

    A discrete random variable has the distribution, for n 1, 2, ...,. Random variables, {Xi:i=1,2,...}, do not depend on N and have the density fx (x) = 0.2e-0.2x for x > 0 and fx (x) = 0, elsewhere. Consider a random sum, 1. Find the expected value of Y. 2. Find the variance of Y. 3. Find the expected value of Y2

  • 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...

  • QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution,...

    QUESTION 2 Let Xi.. Xn be a random sample from a N (μ, σ 2) distribution, and let S2 and Š-n--S2 be two estimators of σ2. Given: E (S2) σ 2 and V (S2) - ya-X)2 n-l -σ (a) Determine: E S2): (l) V (S2); and (il) MSE (S) (b) Which of s2 and S2 has a larger mean square error? (c) Suppose thatnis an estimator of e based on a random sample of size n. Another equivalent definition of...

  • Problem 2: 10 points A random variable, Z, has the Gamma distribution with the density: and...

    Problem 2: 10 points A random variable, Z, has the Gamma distribution with the density: and f ()0, elsewhere. According to the notation in Probability Theory, Z has the distribution Gamma [2. Conditionally, given Zz, a random variable, U, is uniformly distributed over the interval, (0,z) 1. Evaluate the joint density function of the pair, (Z, U). Indicate where this density is positive. 2. Derive the marginal density, fU (u) 3. Find the conditional density of Z, given Uu. Indicate...

  • Question 3 [17 marks] The random variable X is distributed exponentially with parameter A i.e. X~...

    Question 3 [17 marks] The random variable X is distributed exponentially with parameter A i.e. X~ Exp(A), so that its probability density function (pdf) of X is SO e /A fx(x) | 0, (2) (a) Let Y log(X. When A = 1, (i) Show that the pdf of Y is fr(y) = e (u+e-") (ii) Derive the moment generating function of Y, My(t), and give the values of t such that My(t) is well defined. (b) Suppose that Xi, i...

  • 7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the...

    7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...

  • The moment generating function (MGF) for a random variable X is: Mx (t) = E[e'X]. Onc...

    The moment generating function (MGF) for a random variable X is: Mx (t) = E[e'X]. Onc useful property of moment generating functions is that they make it relatively casy to compute weighted sums of independent random variables: Z=aX+BY M26) - Mx(at)My (Bt). (A) Derive the MGF for a Poisson random variable X with parameter 1. (B) Let X be a Poisson random variable with parameter 1, as above, and let y be a Poisson random variable with parameter y. X...

  • The geometric random variable X has moment generating function given by EetX) = p(1 – qe*)-7,...

    The geometric random variable X has moment generating function given by EetX) = p(1 – qe*)-7, where q = 1- p and 0 < p < 1. Use this to derive the mean and variance of X.

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT