![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 Per) = .30 As such Evaluate the following quantities: 2, P(Y = 3) 3. P(x-3) 4. Calculate Px(x 1). Px(2), Px( 3) and Px 4) to generate the marginal distribution Px() Write the marginal distribution in the following form: a 1 5. Calculate the marginal distribution Py (y) again using the form: 6. Calculate marginal probability of Y conditioned on X 2. Py(X-2). Again write in the standard form 7. Calculate marginal probability of Y conditioned on X + Y-3, Pr(vXY 2). Again write in the standard form](http://img.homeworklib.com/questions/1d7925c0-7356-11ea-b928-6d02c0f875b9.png?x-oss-process=image/resize,w_560)
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Consider the following joint probability distribution on the random variables X and Y given in matrix...
Given the following joint distribution of two random variables X and Y (a) Compute marginal distribution...
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
Question 4: Let X and Y be two discrete random variables with the following joint probability...
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...
5. Random variables X and Y have joint probability mass function otherwise (a) Find the value...
5. Random variables X and Y have joint probability mass function otherwise (a) Find the value of the constant c. (b) Find and sketch the marginal probability mass function Py (u). (c) Find and sketch the marginal probability mass function Px (rk). (d) Find P(Y <X). (e) Find P(Y X) (g) Are X and Y independent? 2 内?
The joint probability distribution of the number X of cars and the number Y of buses...
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. y p(x, y) 0 1 2 x 0 0.025 0.010 0.015 1 0.050 0.020 0.030 2 0.125 0.050 0.075 3 0.150 0.060 0.090 4 0.100 0.040 0.060 5 0.050 0.020 0.030 (a) What is the probability that there is exactly one car and exactly one bus during...
15. Problem 15. Show that if pxy (r.v) -Px ()py () for any (r,y) E x x y (independent random vari...
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)...
The discrete random variables X and Y take integer values with joint probability distribution given by...
The discrete random variables X and Y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 Tabulate the distribution and show that a = 0.1. 2 Find the marginal distributions of X and Y. 3 Calculate Cov(X,Y). 4 State, giving a reason, whether X and Y are independent. 5 Calculate E(Y|X = 1).
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 pro...
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...
Problem 47.18 Let X and Y be discrete random variables with joint distribution defined by the...
Problem 47.18 Let X and Y be discrete random variables with joint distribution defined by the following table Y X 2 345 Py(y) 0.05 0.05 0.15 0.05 0.30 0.40 0 0.05 0.15 0.10 0 0.40 0.30 2 px(x 0.50 0.20 0.25 0.05 1 For this joint distribution, E(X) = 285, E(Y) = 1 . Calculate Coy(X,Y)
Given the joint probability table blow,Fill the empty cells. Find the marginal probabilities of given X...
Given the joint probability table blow,Fill the empty cells. Find the marginal probabilities of given X and 0,51 0,03 0,02 0,12 0,74 Px(0) Px(1) Py(0)- Py(l) Py(2)- Find the conditional probabilities given blow P(X-OY-2) P(Y 2X-0)
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
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...
5. Random variables X and Y have joint probability mass function otherwise (a) Find the value of the constant c. (b) Find and sketch the marginal probability mass function Py (u). (c) Find and sketch the marginal probability mass function Px (rk). (d) Find P(Y <X). (e) Find P(Y X) (g) Are X and Y independent? 2 内?
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)...
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...
Problem 47.18 Let X and Y be discrete random variables with joint distribution defined by the following table Y X 2 345 Py(y) 0.05 0.05 0.15 0.05 0.30 0.40 0 0.05 0.15 0.10 0 0.40 0.30 2 px(x 0.50 0.20 0.25 0.05 1 For this joint distribution, E(X) = 285, E(Y) = 1 . Calculate Coy(X,Y)
Given the joint probability table blow,Fill the empty cells. Find the marginal probabilities of given X and 0,51 0,03 0,02 0,12 0,74 Px(0) Px(1) Py(0)- Py(l) Py(2)- Find the conditional probabilities given blow P(X-OY-2) P(Y 2X-0)
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