i need F and C please Definitions (different from text) • The p quantile (or (100p)...
Need help on number 3. Please use method of transformation. Explain if possible. (2)Suppose that X and X2 have joint pdf f(x1, x2) = 2 ,0<x1<x2 < 1, and zero otherwise. Compute the pdf of the random variable Y = (3)Let X-Exp(1) and Y-Exp(1). X and Y are independent. a. Find the pdf of A=(X+Y) and B=(x-7). b. Are A and B independent? C. Find the marginal of A and B
1. Let X1, X2,...,X, be a random sample from each of the distributions having the to lowing pdfs or pmfs: (a) f(x; 0) = 6"e-/x!, r = 0,1,2, ..., 0< < oo, zero elsewhere, where f(0,0) = 1. (b) f(2; 6) = 0.00-110,1)(2), 0 <O< 0o. (c) f(x; 6) = (1/0)e-1/10,00) (2), 0 <$<. (d) f(x; 0) = e-(2-) 110,00) (2), - < < . • For each case, find the ML estimator ômle of 0; • For each case,...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
Let X1,.. ,X be a random sample from an N(p,02) distribution, where both and o are unknown. You will use the following facts for this ques- tion: Fact 1: The N(u,) pdf is J(rp. σ)- exp Fact 2 If X,x, is a random sample from a distribution with pdf of the form I-8, f( 0,0) = for specified fo, then we call and 82 > 0 location-scale parameters and (6,-0)/ is a pivotal quantity for 8, where 6, and ô,...
Please let me know how to solve 7.6.5. 6.5. Let Xi, X2,. .. X, be a random sample from a Poisson distribution with parameter θ > 0. (a) Find the MVUE of P(X < 1)-(1 +0)c". Hint: Let u(x)-1, where Y = Σ1Xi. 1, zero elsewhere, and find Elu(Xi)|Y = y, xỉ (b) Express the MVUE as a function of the mle of θ. (c) Determine the asymptotic distribution of the mle of θ (d) Obtain the mle of P(X...
Only need parts c, e, j, m, and p only need parts c, e, j, m, and p 15. Suppose that X i ~ N(, σ*), i = 1, . . . , n and Zi ~ N(0, 1), i-1, , k, and all variables independent. State the distribution of each of the following variables if it is a "named" distribution or otherwise state "unknown." (a) X1-X2 (i) (b) X2 + 2X3 () Z2 We were unable to transcribe this...
(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...
The density f(x,y) is given by the formula f(x,y) = 8x(x + y), x ≥ 0, y ≥ 0, x + y ≤ 1 and zero otherwise. (a) Find the marginal distributions. (b) Find the conditional distribution of Y given X = x. (c) Find P(X ≤ 1/2, Y ≤ 1/2) (d) Find P(X ≤ 1/2) (e) Find P(Y ≤ 1/2 | X ≤ 1/2) (f) Find P(Y ≤ 1/2 | X = 1/2)
I need the answer for Q 15 15. (i) Find the MLE of 음 from the san ille in Q.12 (i) (ii) Find the ML.E of the distribution function of X, from the sample in Q12 (iii). Let XX, denote a random sample from a population with one of the following densities. Find the MLE of θ. Dfr:0) o a-ok if 0.k and zero otherwise: h known positive integer; (ii) f(r:0-0" (1-0) if r 1.2 . and zero otherwise; 0...
I need help on part b, c, d, and f. Suppose X follows a N3( μ, Σ ) distribution with 784 504-200 mean vector μ= | 130 | and covariance matrix 175 200 0 1600 a Find P(X, > 139). b Find p 12 Cor(X1. X2) c) Find P(X2> 139 |X1-103) "Hint": (Xi.X2) jointly follow a bivariate normal distribution d) Find P(X2< X e) Find P(X2<X3) Find P(X2〈 145〈X3) "Hint": P(X2〈145 & 145 〈 X 3) g)find P(X1 + 2X2+3X3>...