Homework Answers
| x | |||
| 1 | 2 | ||
| y | 1 | 0.04 | 0.16 |
| 2 | 0.48 | 0.32 |
formula
P(X=x, Y =y) = P(Y=y|X= x) P(X = x)
| x | |||
| 1 | 2 | ||
| y | 1 | =0.2*0.2 | =0.8*0.2 |
| 2 | =0.8*0.6 | =0.8*0.4 |
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Consider a pair of discrete random variables X and Y. suppose that the marginal distribution of...
The table below gives the joint probability mass function of a pair of discrete random variables...
The table below gives the joint probability mass function of a pair of discrete random variables X and Y. Pxr(x,y) 12 3 P) 10.30 0.05 0.15 2 0.10 0.05 0.35 px(x) Complete the marginal distributions in the table above. . Are X and Y independent? Yes Check
pleaze help me fast 2. Let X and Y be discrete random variables with joint probability...
pleaze help me fast
2. Let X and Y be discrete random variables with joint probability mass function X=1 X=5 Y=1 5a За Y=5 4a 8а a. What is the value of a? b. What is the joint probability distribution function (PDF) of X and Y? c. What is the marginal probability mass function of X? d. What is the expectation of X? e. What is the conditional probability mass function of X given Y = 1? f. Are X...
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)
Ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that t...
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...
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...
Consider a pair of independent random variables X and Y with identical marginal p.m.F.'s (1-0) for...
Consider a pair of independent random variables X and Y with identical marginal p.m.F.'s (1-0) for z E 10, 1,2,... otherwise {(1-0 gu otherwise 1,2,..) pr(v) (This is an alternative way of defining the geometric distribution.) Complete the derivation of the distribution of Z X +Y below. (1-0) Complete the derivation of the conditional distribution of XZ If we know that X and Zz,then If we know that Zthen X can take any value between below and Complete the derivation...
1. Suppose you have two random variables, X and Y with joint distribution given by the...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
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).
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass...
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass function P(x, y, z) given below. Be sure to full justify your answers and show ALL work. P(0,0,0) = 2,3 P(0,0,1) 33 P(0,1,0) = P(1,0,0) = 32 P(1,0,1) = P(1,1,0) = 32 a. Find the marginal probability mass function for 2, pz(2). b. What is E[X | Y = 0]? P(0,1,1) = 4 P(1,1, 1) = 32
a,b,c,d 1. Suppose random variables X and Y appear together in the following way: X 20...
a,b,c,d
1. Suppose random variables X and Y appear together in the following way: X 20 21 0 Y 422 41 Assume that each observation is equally likely (a) Find the joint probability mass function, fx.y (b) Find the marginal probability mass function, the distribution function, and the expectation of Y (e) Find the conditional expectation of Y given X =x, for each value of x. (d) Find the conditional expectation of Y given X. Find the expectation of the...
The table below gives the joint probability mass function of a pair of discrete random variables X and Y. Pxr(x,y) 12 3 P) 10.30 0.05 0.15 2 0.10 0.05 0.35 px(x) Complete the marginal distributions in the table above. . Are X and Y independent? Yes Check
pleaze help me fast
2. Let X and Y be discrete random variables with joint probability mass function X=1 X=5 Y=1 5a За Y=5 4a 8а a. What is the value of a? b. What is the joint probability distribution function (PDF) of X and Y? c. What is the marginal probability mass function of X? d. What is the expectation of X? e. What is the conditional probability mass function of X given Y = 1? f. Are X...
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)
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...
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...
Consider a pair of independent random variables X and Y with identical marginal p.m.F.'s (1-0) for z E 10, 1,2,... otherwise {(1-0 gu otherwise 1,2,..) pr(v) (This is an alternative way of defining the geometric distribution.) Complete the derivation of the distribution of Z X +Y below. (1-0) Complete the derivation of the conditional distribution of XZ If we know that X and Zz,then If we know that Zthen X can take any value between below and Complete the derivation...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass function P(x, y, z) given below. Be sure to full justify your answers and show ALL work. P(0,0,0) = 2,3 P(0,0,1) 33 P(0,1,0) = P(1,0,0) = 32 P(1,0,1) = P(1,1,0) = 32 a. Find the marginal probability mass function for 2, pz(2). b. What is E[X | Y = 0]? P(0,1,1) = 4 P(1,1, 1) = 32
a,b,c,d
1. Suppose random variables X and Y appear together in the following way: X 20 21 0 Y 422 41 Assume that each observation is equally likely (a) Find the joint probability mass function, fx.y (b) Find the marginal probability mass function, the distribution function, and the expectation of Y (e) Find the conditional expectation of Y given X =x, for each value of x. (d) Find the conditional expectation of Y given X. Find the expectation of the...
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