Question: a) The joint probability distribution of two discrete random variables X and Y is given below. X = 1 X = 2 X =

a) The joint probability distribution of two discrete random variables X and

a) The joint probability distribution of two discrete random variables X and Y is given below. X = 1 X = 2 X = 3 X = 4 Y = 1 0.06 0.02 0.2 0.18 Y = 2 0.12 0 P 0.06 Y = 3 0 0.08 0.16 0 i. ii. Find the probability p. [2 marks] Find the marginal distributions fx (x) and fy (y) iii. Find the conditional distribution fx| x=2 [4 marks] iv. Find P(XY). b) The probability density function of a continuous random variable T is given by f(t) = {kt sin(t), 0t1 Find k. 0, otherwise [4 marks] [3 marks] [7 marks] c) The cumulative distribution function of a random variable is given by F(x) = Szexp (), 1- exp(--), x b Where b is a positive constant and the median of the distribution is . Find the upper quartile of this distribution. [7 marks]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

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 Marketing Questions!

What interest rate would be necessary for$5,750 investment to growto$8,850 in an account compounded monthly for 11 years?

Explain the concept of "lazy loading" in memory management. How does it relate to demand paging, and what are the benefits and potential drawbacks of this approach ?

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

(From MS 6.18) Find the numerical value of c to 4 decimal places. 6.18 Let X and Y be two continuous random variables with joint probability density Ice-( xty) if O s x 05 12 3 .02 09 07 10 A 08 01...

Find the numerical value of The joint probability distribution for two discrete random variables X and Y is given by the formula (see attached). (From MS 6.10) Find the numerical value of | > |...

The joint probability distribution for two discrete random variables, X and Y, is given by the formula Verify that the properties of a bivariate probability distribution are satisfied. p(x, y) =...

2.38. A coin is tossed three times. If X is a random variable giving the number of heads that arise, construct a table showing the probability distribution of X. 2.39. An urn holds 5 white and 3...

GIVE DETAILED WORKING IN ALL QUESTIONS. Suppose that a game is to be played with a single die assumed fair. In this game a player wins $20 if a 2 turns up, $40 if a 4 turns up; loses $30 if a 6 turns...

Question 5 The following table presents the joint probability distribution of two discrete random variables X and Y. x 1 2 3 0 0.10 0.21 0.06 y 1 0.05 0.10 0.11 2 0.02 0.11 0.24 a) Graph the...

A survey conducted by the Consumer Reports National Research Center reported, among other things, that women spend an average of 1.2 hours per week shopping online. Assume that hours per week...

Strategy for Overcoming an Unfavorable Reaction: ATP-Dependent Chemical Coupling The phosphorylation of glucose to glucose 6-phosphate is the initial step in the catabolism of glucose. The direct...

For the most recent December 3 1 , for almost all Savings Institutions ( SIs ) , the predominate type of collateral for Real Estate mortgage loans that SIs originated was for _ _ _ _ _ _ _ _ _ ....

Many Whites argue that their resistance to affirmative action and diversity programs is due in part to their families' history of not owning slaves or their not having practiced discrimination2. What...

The Mutron Company is thinking of marketing a new drug used to make pigs healthier. At the beginning of the current year, there are 1,000,000 pigs that could use the product. Each pig will use...

Following is a list of various costs incurred in producing replacement automobile parts. With respect to the production and sale of these auto parts, classify each cost as either variable, fixed, or...

Hiramatsu Exports, Inc., is a wholesaler of Japanese goods. By the end of 20X0, the companys cash balance had dropped to 9 million, despite net income of 254 million in 20X0. Its transactions...

Mega Screens, Inc., reports net sales of $3,200,000, cost of goods sold of $2,000,000, and income tax expense of $150,000 for the year ended December 31, 2015. Selected balance sheet accounts are as...

Which of the following best explains the key components you would use to analyze key market segments? Market segment analysis is based on demographic, geographic, psychographic, and behavioral...

Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x? Explain or give an example.

According to Harpers Index, 50% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected. (a) What is the probability that 12 or more are serving...

The Sand Canyon Archaeological Project edited by W. D. Lipe and published by Crow Canyon Archaeological Center contains the stem-and-leaf diagram shown in Figure 2-19. The study uses tree rings to...

Write a succinct statement that distinguishes marketing communication from marketing communications.

Where might significant differences arise in the communication needs of the provider and the consumer or buyer? How might managers deal with this problem?

Examine Table 7.11. Carry out a more detailed analysis of the advantages and disadvantages of different means for communicating, using specific information wherever possible.