(1 point) If Y-Σǐn 1 X, and every Xi is i.i.d with distribution binomial(n, p), find...
1 point) If YX and every X, is i.i.d with distribution binomial(n, p), find the MGF of Y M(t) = What is the distribution of Y? Select all that apply. There may be more than one correct answer. DA, binomial(rn * n, p) B. binomial(n, m*p) | | C. binomial(m, p) D. negative binomial(n,p) E. negative binomial(m,p) F. negative binomial(n, m* p) G. binomialn,p) OH. negative binomial(m * n, p) I. None of the above
(1 point) If Y-LX, and every X, is ii.d with distribution binomial(n, p), find the MGF of Y M(t) What is the distribution of Y? Select all that apply. There may be more than one correct answer A. binomial(n, m p) B. negative binomial (n, p) C. negative binomial(m,p) D. binomial (n, p) E. negative binomial(n, m * p) F. binomial(m *n,p) G. binomial(m, p) OH. negative binomial(m * n, p) I. None of the above (1 point) If Y-LX,...
21 (1 point) If Y X and every Xi is i.i.d with a chi-squared distribution with 14 degrees of freedom, find the MGF of Y М()- What is the distribution of Y? Select all that apply. There may be more than one correct answer. А. gатта(а - 147, 8 В. датта(а — 2, В — 294) с. датта(а — 1,8— 1/147) D. gamma(a 1, B 1/294) E. chi squared(df 294) F. еzрoпential(A — 204) G. exponential(A 147) H. chi squared(df...
0.2e ( poimt Given the M randmvariable X is MO). t0Provide the name of the distribution of X, as well as its provide the name of the distrbon of X, as well as is parameters Select all that apply. There may be more than one correct answer. A. negative binomial (n 1,p 0.2) OC. geometric(p 0.8) B. geometriclp 0.2) D. negative binomial(n-1, p-0.8) E. binomial(n-1,p-0.2) - F. binomial(n-1, p-0.8) G. bernoulli(p 0.2) H. bernoulli(p 0.8) I. None of the above
(1 point) If Y is binomial(n, p), find the MGF of Y. M(t) If n = 13 and p = 0.2, differentiate the MGF you found above to find the first 3 moments of Y about 0. 1st Moment: 2nd Moment: 3rd Moment: Using the moments above, calculate the variance of Y. var(Y) = (1 point) If Y is binomial(n, p), find the MGF of Y. M(t) If n = 13 and p = 0.2, differentiate the MGF you found...
6. Suppose C) ~ N (C), Ģ:: ru). Find the distribution of X|Y. Hint use the formula p p(y) 7. Consider i.i.d. observations Xi, .., Xn ~ N(H, 1) (a) Compute E(XiX). Hint: use the above problem, and find the conditional distribution of Xi given X first (b) Compute E (ix)
(1 point) Given the MGF of random variable Wis M(t) = €2.4+-+15t provide the name of the distribution of W, as well as its parameters. Select all that apply. There may be more than one correct answer. A. normal(u = 2.4, o2 = 15) B. normallu = 15, o2 = 2.4) C. gamma(a = 4.8,B = 15) D. gamma(a = 15, B = 4.8) E. normal(u = 4.8, 02 = 15) OF. gamma(a = 15, B = 2.4) G. normallu...
3, Let X, X2,X, be independent random variables such that Xi~N(?) a. Find the distribution of Y= a1X1+azX2+ i.(Hint: The MGF of Xi is Mx, (t) et+(1/2)t) + anXn +b where a, 0 for at least one b. Assume = 2 =n= u and of- a= (X-)/(0/n) ? Explain. a. What is the distribution of The Sqve o tubat num c. What is the distribution of [(X-4)/(0/Vm? Explain.
(b) For n = 100, give an approximaation for P(Y> 100) (c) Let X be the sample mean, then approximate P(1.1< 1.2) for -100. 2. Consider a random sample XX from CDF F(a) 1-1/ for z [1, 0o) and zero otherwise. (a) Find the limiting distribution of XiI.n, the smallest order statistic. (b) Find the limiting distribution of XI (c) Find the limiting distribution of n In X1:m- 3. Suppose that X,,, are iid. N(0,o2). Find a function of T(x)x...
Recall that the binomial distribution with parameters n and p is governed by Let n be some known number, say n-1000. Then the pmf is 1000 f (y) p)1000-, Write this as an exponential family of the form 1000 fp (v)-h() exp (n (p)T(v) p) where h () then enter η (p) T (y) and B (p) below. To get unique answers, use 1 as the coefficient of y in T (s). T (v)- B(p) Recall that the binomial distribution...