4. Suppose the moment generating function (mgf) of any random vector (X, Y), is given by M(t1, t2), then the mgf of X, Mx(t) = M(t, 0). True or false, explain.
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- Please do not copy other's work I will be very very appreciate!!Probability and Statistics for Engineering and the Sciences 9th Ed. By. Jay Devore ISBN: 9781305251809 Chapter 2 #2 (D & E parts only) 2) Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. C ={RRL, RLR, LRR, RRS, RSR, SRR} (previously given answer needed to answer part E) d) List all outcomes in the event D that exactly two vehicles go in the same direction. e) List outcomes in D’, C ∪D, and C ∩ D.Which of the following is the autocorrelation function Rz (t1, t2) of a Poisson Random process with an arrival rate A? (assume t2 > t1) a. Rz(t1, t2) = X²t;+ At1 b. R (t1, t2) = 1²t;t2 + Atq c. Rz (t1, t2) = X²t} + Atz d. Ra (t1, t2) = ²tyt2 + At1
- 2 Let B be the (k + 1) × 1 vector of OLS estimates. (i) Show that for any (k + 1) × 1 vector b, we can write the sum of squared residuals as SSR(b) = û'û + (ß – b)'X'X(ß – b). {Hint: Write (y – Xb)'(y – Xb) = [û + X(ß – b)]'[û + X(ß – b)] and use the fact that X'û = 0.} Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). hat any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. (ii) Explain how the expression for SSR(b) in part (i) proves that B uniquely minimizes SSR(b) over all possible values of b, assuming X has rank k + 1.Part II: Sections 2.1 2.7 7. Suppose that X is a discrete random variable with pmf f(x) =D c.14-피 . 뉴- 21 for r=-3, 3, 6, where c is a constant. (a) Find c. Compute E ( ~LX +) (b) 3.Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
