(i)
Sample space={000,001,010,100,011,101,110,111}
Q1] (20 Marks) Three-digit numbers constructed using only 0's and 1's. Let X(s) - No. of...
15. Problem 15. Show that if pxy (r.v) -Px ()py () for any (r,y) E x x y (independent random variables) then: EIXY-EX] E[Y: factorazibility of crpectation values; b) sex.r-sx)+s(): aditinity of entropy Note that pxy (r, y) denotes the probability density function of the joint random variable (x, Y), while px (a) and py (u) are the marginal probability density functions of and Y, respectively. The Shannon eatropy (messured in units of nats) of the joint system (X. Y)...
Consider the following joint probability distribution on the random variables X and Y given in matrix form by Pxy P11 P12 P13 PXY-IP21 p22 p23 P31 P32 P33 P41 P42 P43 HereP(i, j) P(X = z n Y-J)-Pu represents the probability that X-1 and Y = j So for example, in the previous problem, X and Y represented the random variables for the color ([Black, Red]) and utensil type (Pencil,Pe pblackpen P(X = Black Y = Pen) = P(Black n...
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...
Please show how did you came up with the answer, show formulas
and work. Also, please do Parts e to i. Thank you so much
1. Consider the following probability mass function for the discrete joint probability distribution for random variables X and Y where the possible values for X are 0, 1, 2, and 3; and the possible values for Y are 0, 1, 2, 3, and 4. p(x,y) <0 3 0 4 0.01 0 0 0.10 0.05 0.15...
(a) Sketch the region in the (x,y) plane where ??,?(?, ?) ≠
0.
(b) Find the marginal probability density functions ??(?) and
??(?) of ? and ? respectively.
(c) Are X and Y independent?
(d) Find P(Y>X).
(e) Let y be some real number in the range 0 ≤ y ≤ 1. Find the
conditional probability density function ??|?(?|?).
(f) Find ?[?|? = ?] (where ? is some real number in the range 0
≤ ? ≤ 1).
The joint...
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
I just need the second problem done. Problem #2 refers to the
problem #1.
Problem # 1. Let discrete random variables X and Y have joint PMF cy 2,0,2 y=1,0, 1 otherwise = Px.y (x, y) 0 Find: a) Constant c X], P[Y <X], P[X < 1 b) P[Y 2. Let X and Y be the same as in Problem # 1. Find: Problem a) Marginal PMFs Px() and Py(y) b) Expected values E[X] and E[Y] c) Standard deviations ox...
sucCesses isk. 6142 Let S consist of the 10 decimal digits. Suppose that a number X is chosen according to the discrete uniform distribution on S and then a number Y is chosen according to the discrete uniform distribution on {X, X +1,.. . .9}. a) Determine the conditional PMF of X given Y marginal PMF of Y and the joint PDF of X and Y b) Evaluate the conditional PMF in part (a), given Y = 6. = y...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 – x)y for 0 < x < 1, (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y. (d) Find Pſy < 81/2],P[X<Y]. (e) Are X and Y independent? (f) Find the correlation and covariance of X and Y. (g) Determine whether X and Y are uncorrelated. (h) Find fy(y|x) (i) Find E[Y|X = x]...