a random a distribution with-p f for a-lnxio o--othenuse Find the marginal p ot D
8 otherwise for some constant k. Find: a) the marginal distribution of Y; b) P(Z<}\Y = ). 8. The random variable X has a uniform distribution on (0,1). Given that X = 1, the random variable Y is binomial with parameters n = 5 and p = r. a) Find E(Y) and E(Y?). b) Find P(Y = y and a < X < = + dx). c) Find the density of X given Y = y. Do you recognize it?...
Let x1, x2,..,xn represent a random sample from a distribution with pdf f(x)=px(1-p)1-x for x=0,1 and 0<p<1. Find MLE for p. Choose an answer: n O b. 1/29=1*; O d. None are correct 59
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50) 0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y |X = x. (d) Find P(Y < 3|X = 1). Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
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,...
Let X, X₂ X3 X4 ~ Np (M, E) random vectors. a) Find the marginal distribution for each of the random rectors V = 3x + x +4x,-4 xe V2 = 13 x + 1 3 X 2 - 1 3 X3 - 1 344 b) Find the distribution of the random vectors V, and V2. c) Find the joint density of the random vectors V, and a defined in ca) and (b).
The random variable x has the following discrete probability distribution. Complete parts a through f Question Help O The random variable x has the following discrete probability distribution. Complete parts a through f. P(x) 622 8 0.4 0.2 9 0.2 0.1 a. List the values x may assume. DODO. (Use ascending order.) b. What value of x is most probable? c. Display the probability distribution as a graph. Choose the correct graph below. OA. OB Oc. OD 071 LUH >...
3. Consider a discrete random variable X which follows the geometric distribution f(x,p) = pr-1(1-p), x = 1.2. . . . , 0 < p < 1. Recall that E(x) (1-p) (a) Find the Fisher information I(p). (b) Show that the Cramer-Rao inequality is strict e) Let XX ~X. Find the maximum likelihood estimator of p. Note that the expression you find may look complicated and hard to evaluate. (d) Now modify your view by setting μ T1p such that...
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Given the following joint distribution of two random variables X and Y (a) Compute marginal distribution PX(x) (b) Compute marginal distribution PY(y) (c) What is the conditional probability P(Y | X = 2)? 20.10 0.05 0.15 0.10 0.10 4 0.04 0.02 0.06 0.04 0.04 6 0.04 0.02 0.06 0.06 0.02 8 0.02 0.01 0.03 0 0.04