Question: Consider two rolls of a fair six-sided dice. let x be the result of the first roll and y the result of the second roll

Consider two rolls of a fair six-sided dice. let x be the result of the first roll and y the result of the second roll and z be the sum of the two rolls

a) Which pairs of variables if any are positively correlated?

b) Which pairs of variables if any are uncorrelated?

c) Which pairs of variables if any are negatively correlated?

d) Which pair of variables if any are independent

e) Let W=X-Y, how are W and Z correlated? Are they independent? Justify your answer?

Step by Step Solution

★★★★★

3.36 Rating (159 Votes )

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 Biology Questions!

Two fair dice are rolled. Let X be the sum of the dice. What is the expected value of X?

Let be the sum of independent rolls of a fair (cubicle) die. (a) (b) Find lim Pr(X is a multiple of 3) Find lim Pr(X is a multiple of 5)

Let be the sum of independent rolls of a fair (cubicle) die. (a) Is X [n] a Markov chain? (b) Define a new process according to Y[n] = X[n] mod 3. That is, Y[n] { 0, 1, 2} is related to X [n] X [n] =...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

s: Chapter 4: 24. a) A lot of 25 items is to be inspected by means of a two-stage sampling plan. A sample of five items is drawn. If one or more is bad, the lot is rejected. If all are non-defective,...

Q #1 5. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.1.008. MY NOTES ASK YOUR TEACHER Over the past decade, there has been a strong positive correlation between teacher salaries and...

PLEASE SOLVE ON PAGE 2) (15 points) Paul deposits $50,000 in a fund that pays 6% per year compounded monthly. He plans to withdraw $1,500 per month for the first two years. What equal amount can he...

Simply put, it gave the impression that things were three times larger than they actually were. He improved the design of the telescope so that it could zoom in eight times and then thirty. The...

Makeup product (e.g. any one item such as eyeshadows, foundation etc. ) Hint: How will you obtain feedback about competitors' similar products? Use survey or other method for collecting customer...

During July, the following are given: Standard unit price 12.50 Standard Quantity Allowed for actual production 6,300 units Actual unit purchase price Quantity purchased and used for production...

An RFP is used for what type of procurement? Give an advantage and a disadvantage of the RFP process

You are the area manager of several starbucks and you make all of the decisions regarding land, building, and equipment. Additionally you are responsible for all of the profits of the starbucks in...

Liquidity, solvency and financial flexibility are important concepts related to cash flow, explain?

Use the method of Example 4.29 to compute the indicated power of the matrix. 1 0 1

Email checking. The percent of time on a workday that employees at a company spend checking email can be modeled by the following function: a. Why is this Beta distribution? b. What are the...

Roll two 4-sided dice and let X denote the sum. a. Draw the mass of X. b. Draw the CDF of X.

On a strand of lights, the expected number of lights that fail to work correctly is 20. a. What is an upper bound on the probability that 30 or more lights fail to work? b. If the standard deviation...

Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming Americas Cup race. They race over a part of the course several times. Below are a sample of times in...

Commercial Bank and Trust Company is studying the use of its automatic teller machines (ATMs). Of particular interest is whether young adults (under 25 years) use the machines more than senior...

The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold...