Question: Let X and Y be random variables with joint distribution showing in the following figure. P(x, y) 1 1 0 2 0.10 3 0.40

Let X and Y be random variables with joint distribution showing in the following figure. P(x, y) 1 1 0 2 0.10 3 0.40 Y I 3 4 0.06 0.10 0.04 0.04 0 2 0.06 0.10 0.10 0 (a) Find the marginal distribution of X. (b) Find the marginal distribution of Y. (c) Are X and Y independent? State your reasons.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To find the marginal distributions of X and Y from the joint probability distribution Px y you sum a... 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!

Let X and Y be random variables with joint pdf fX,Y (x, y)=k, 0 x 1, 0 y 1, 0 x + y 1 Give a geometric argument to show that X and Y are not independent.

Let X and Y be random variables with joint density function Find the expected value of Z = /X2 + Y2.

Let X and Y be random variables with finite variance. Prove that |(X, Y)| = 1 implies that there exist constants a, b, and c such that aX + bY = c with probability 1. Use Theorem 4.6.2 with U = X X...

Let X1, . . . , Xn be i.i.d. random variables with Poisson distribution P(Xi = k|) = e k k! , k = 0, 1, 2, . . . . Suppose the intensity parameter has a Gamma(, ) distribution. (a) Find the posterior...

21. Let X and Y be continuous random variables with joint probability density function Find the conditional expectation of Y given that X = x. f(x, y) = Jn(n-1)(y-x)-2 if 0x y 1 = otherwise.

Exercise 6.55 Let X and Y be random variables with joint density function f (x, y) = ( 1 4 e1 2 (x+y) if x, y > 0, 0 otherwise. Show that the joint density function of U = 1 2 (X Y ) and V = Y is...

6.6 Conditional density functions 95 Exercise 6.55 Let X and Y be random variables with joint density function f (x, y) = ( 1 4 e1 2 (x+y) if x, y > 0, 0 otherwise.

Let X and Y be two jointly continuous random variables with joint PDF a. Find the marginal PDFs, f X (x) and f Y (y). b. Find P(X > 0,Y c. Find P(X > 0 or Y d. Find P(X > 0|Y e. Find P(X + Y > 0)....

Let X and Y be two jointly continuous random variables with joint PDF a. Find R XY and show it in the xy plane. b. Find the constant c. c. Find marginal PDFs, f X (x) and f Y (y). d. Find P(Y x/2)....

Suppose that the random variable X has an exponential distribution with parameter ? > 0. (i) What are the probability density function, fX(x), and the probability distribution function, FX(x), for...

The menagement of Sege instrument Company had concluded, with the concurrence of its independent auditors, that results of operations would be more fairly presented if Sage changed its method of...

You will be folding a sheet of paper in half (direction doesn't matter) and recording the number of sections created after each step in a table. Before you fold the paper at all, how many sections...

Kaladin and his boyfriend are in a fight. Kaladin decides to use 'the silent treatment' to show his boyfriend how mad he is. Which of the four unproductive approaches to conflict resolution...

SCMP Module 5, Module Culminating Assignment. (MCA) Workplace review in a case study format for the given below topics (from executive summary to monitor and control). As the focus is on strategic...

1. Referring to Exhibit 4, compute the annual percentage change in net income per common share-diluted (second numerical line from the bottom) for 1998-1999, 1999-2000, and 2000- 2001. Date Range...

tony soprano, leader of the soprano crime syndicate of NJ, waskilled by one of his own henchmen. detective vine interviews themen and determines that all were lying except for one, based onwhat he...

The totals from the first payroll of the year are shown below. Total Earnings FICA OASDI FICA HI FIT W/H State Tax Union Dues Net Pay $36,195.10 $2,244.10 $524.83 $6,515.00 $361.95 $500.00 $26,049.22...

Explain the buyers position in a typical negotiation for a business. Explain the sellers position. What tips would you offer a buyer about to begin negotiating the purchase of a business?

Let X 1 , X 2 , . . . , X n be a random sample of size n from the Poisson distribution, p X (k; ) = e k /k!, k = 0, 1, . . .. Show that = X i is an efficient estimator for .

Use the method of moments to estimate in the pdf f Y (y; ) = ( 2 + )y 1 (1 y), 0 y 1 Assume that a random sample of size n has been collected.

Let Y1, Y2, . . ., Yn be a random sample from the exponential pdf fy(y) = ey, y 0. What is the smallest n for which P(Ymin 0.9?

Another useful distribution that is based on the normal is the lognormal distribution. Among other applications, this distribution is used by environmental engineers to represent the distribution of...

If the number of chocolate chips in a chocolate-chip cookie follows a Poisson where the average is 3.6 chocolate chips per cookie, what is the probability of finding no chocolate chips in a given...

You are an executive at Procter and Gamble and are about to introduce a new product. Your boss has asked you to predict the market share (Q, a proportion between 0 and 1) that the new product will...