4. (20 points) Xavier and Yvette are real estate agents. Let X denote the number of...
4. (20 points) Xavier and Yvette are real estate agents. Let X denote the number of houses that Xavier will sell in a month and let Y denote the uber of houses Yvette will sell in a month with the following joint probabilities of (X,Y) 0.1 0.2 0.2 0.3 0.1 (a) Find the unconditional mean E(Y) (b) Find the unconditional variance V (Y) (c) Find the conditional means E (YlX-0) and E(Y|X = 1). (d) Find COV (X, Y)
Moving to another question will save this response. Question 10 Question 1 3.22581 points Xavier and Yvette are two real estate agents. Let X and Y denote the number of houses that Xavier and Yvette will sell next month, respectively. The joint distribution is given below: х 0 1 2 0 0.2 0.1 0.05 1 0.1 0.20 0 2. 0 0.15 0.20 Find the probability that Yvette sells no more than I house if Xavier sells no more than I...
I need help by solving this Problems 133 5.3 Let X and Y have the following joint PMF 0.1 0.1 0.1 0.1 0 0.0 0.1 0.2 0.3 o-一ㄒㄧㄒㄧ丁 a. What are the marginal PMFs of X and Y? b. What are the conditional probabilities (computed directly) of X given Y and Y giw X (compute them directly)? c. What are the conditional probabilities of Y given X from the conditional probabilit of X given Y using Bayes theorem? Using the...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer. (20 points) Consider the following joint distribution of X and...
2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3 times) a technician is called on an emergency call. The joint probability distribution fxy(x, y) is given by 1 0.05 0.05 0 0.05 0.1 0.2 0.1 0.35 0.1 (a) Evaluate the marginal pdf and the mean of X (b) Evaluate the marginal pdf and the mean of Y....
Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3 times) a technician is called on an emergency call. The joint probability distribution fxy(x, y) is given by 1 2 y 0.05 1 0.05 0.1 2 0.05 0.1...
Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (b) Compute E(X) and the conditional expectation E(X|Y= 1).
4. Let X denote the number eggs hatched out of Y eggs laid by a particular parasite. The joint pmf of (X, Y) is given by A(1-0) e ,for x 0, 1, 2,.., y , and y = 0,1,2, .,00 Px,y (x, y)= 1 -6 = 0, otherwise where A> 0 and 0< 0<1 are unknown constants. (a) Find the marginal pmfs of X and Y. Are X and Y independent? (b) Find the conditional pmf of X|Y = y...
Problem 2: (8 points) Let X be the number of hoses being used on the self-service and Y that being used on the full-service on an Island. The joint p.m.f. of X and Y is given by 1 y 0 2 0 0.1 0.04 0.02 0.08 0.2 0.06 2 0.06 0.14 0.3 1 (a) Show that this is a valid joint p.m.f. [1] (b) Fill out the table with the marginal distributions of X and Y. [2] (c) Calculate E(X),...