Question: Random variables X and Y have the joint PMF (a) What is the value of the constant c? (b) What is P(Y < X)? (c)

Random variables X and Y have the joint PMF

c(x + y), if x E {1,2, 4} and y E {1,3},

(a) What is the value of the constant c?

(b) What is P(Y

(d) What is P(Y = X)?

(e) What is P(Y = 3)?

(f) Find the marginal PMFs pX(x) and pY (y).

(g) Find the expectations E[X], E[Y] and E[XY].

(h) Find the variances var(X), var(Y) and var(X + Y).

(i) Let A denote the event X ≥ Y. Find E[X | A] and var(X | A).

c(x + y), if x E {1,2, 4} and y E {1,3}, 0, otherwise. PX,y(x, y)

Step by Step Solution

★★★★★

3.49 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To solve the problem well follow each part step by step a What is the value of the constant c The joint PMF must sum to 1 over all possible values Calculate beginalign sumx124 sumy13 cx2 y2 c12 12 12 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The independent random variables X and Y have the means and standard deviations as given in the following table. Use these parameters to find the expected value and SD of the following random...

Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y 3). (b) Find the marginal PDFS of Y and X. f(x, y) = 2exy0xy

Let the random variables X and Y have the probability distributions listed in Table 15. Determine the probability distributions of the random variables in Exercises. 1. X2 2. Y2 3. X - 1 4. Y - 15 5....

Please help asap Two random variables X and Y have the joint pmf Pyy (x, y) given below Pyy (x, y) y = 1 y = 2 y = 3 x =-1 O 0.01 O O x = 0 0.09 0.09 x = 1 O no O 1. What should the missing value in...

Which of the following could be quantified as a Bernoulli random variable? a) number of persons in a hospital ward with terminal diagnoses. b) weights of deliveries at a supermarket. c) square foot...

IE300 BL1 - Analysis of Data Assignment #5 Due Date: October 16, 2015 INSTRUCTIONS: This assignment must be turned in during the first ten minutes of lecture (11:00-11:10AM in 103 Transportation) on...

solve these practice problems The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used...

For continuous random variables X and Y , taking on continuous values x and y respectively with probability densities p(x) and p(y) and with joint probability distribution p(x, y) and conditional...

solve these problems The relative conductivity of a semiconductor device is determined by the amount of impurity "doped" into the device during its manufacture. A silicon diode to be used for a...

Variable Costs, Contribution Margin, Contribution Margin Ratio: Super-Tees Company plans to sell 18,000 T-shirts at $24 each in the coming year. Product costs include: Direct materials per T-shirt...

An analysis of the transactions made by Blossom & Co., a certified public accounting firm, for the month of August is shown below. The expenses were $550 for rent, $3,800 for salaries and wages, and...

A company plans to configure a vessel's journey in Dynamics 365 Supply Chain Management by using the landed cost functionality. The company needs to track the details of each step of the journey...

10 Which of the following is NOT a disadvantage of virtual integration in supply chains? 1 point Often variations in the IT capabilities and existing level of infrastructure across supply chain...

ACTIVITY 3: PREPARE ME Below are the Income Statement and Balance Sheet of Hobert Supply and Services. Using these data, prepare the company's Statement of Changes in Equity. Herbert Supply and...

A data professional works on a financial audit. During the verification process, they keep in mind the big picture view of confirming that the company's financial statements comply with accounting...

Name three cause of catalyst deactivation and how they can be prevented?

Show that the peak of the black body spectrum as a function of ? is given by eq. (22.14) kg T Wmax = 2.82

1. If the selected 25 transactions are treated as Bernoulli trials, the resulting binomial calculations will be in error because of sampling from a finite population. 2. The binomial model for this...

Which has larger variance, the prices of items in a grocery or the prices of cars at a new car dealer? Which has the larger coefficient of variation?

The following table summarizes findings from a study done by Apple concerning working conditions in factories operated by its suppliers.9 Under pressure from consumers concerned about working...

Various attempts have been made to reduce the accounting diversity that exists internationally. This process is known as convergence and is discussed in more detail in Chapter 3. The ultimate form of...

In what way is the IASB's Framework intended to assist firms in preparing IFRS-based financial statements?

Refer to the income statements presented in Exhibits 2.9, 2.10, 2.11, 2.12, and Problems 2.13 for Callaway Golf Company, Siidzucker AG, Cemex S.A.B. de CV, Sol Melia SA, and Thai Airways. Required:...