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You are at a table at a casino with a gambling game. In the game you spin two spinners. Spinner #1 has 4 equal spaces numbered 1,2,3,4. Spinner #2, has only two equal spaces with the numbers 1 and 3. To play the game, you have to pay $4 dollars. Regardless of whether you win or lose you have to pay the $4. There are two different bets you can make that are related to the sum of the two spins (number from Spinner #1 + number from Spinner #2). Shown below are the two different bets and amounts associated with winning each.

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Bet 1: You win $8 if the sum of Spinner #1 and Spinner #2 is less than 5?

Bet 2: You win $12 if the sum of Spinner #1 and Spinner #2 is greater than 5?

What is the sample space? Hint: this is the number of different outcomes where order does matter. So getting a 1 on Spinner #1 and 3 on Spinner #2 is a distinct outcome from the reverse.?

What is the probability of winning Bet 1? What is the probability of winning Bet 2??

What is the expected value of Bet 1? What is the expected value of Bet 2? Which is the better bet? Would you break even (i.e. not lose any money) with either bet??

For Bet 2, how much would you have to earn to exactly break even (neither lose nor win money in expectation)??

Now imagine for Bet 1 you only have to pay the $4 to play if you lose. What is the expected value of Bet 1 now? Would you break even??

PROBLEM 4 Covariance and Correlation Based on the following information, calculate the expected return and standard deviation of each of the following stocks. Assume each state of the economy is equally likely to happen. What are the covariance and correlation between the returns of the two stocks? State of Economy Return on Stock A Return on Stock B Bear .108 -.067 Normal .126 .113 Bull .064 .276 Question 1. Consider the Covariance and Correlation 'om a random sample of size n, from two random variables. How many statements are correct? 0 l 2 3 4 Statement A. Covariance and Correlation are statistical measures of the linear relationship between two variables. Statement E. Correlation can take on any value. Covariance ranges between minus one and plus one. Statement C. For a sample size of 11, Population Covariance is equal to Sample Covariance times ((nl )fn). Statement D. Covariance can be considered a relative measure of a linear relationship. Correlation can be considered an absolute measure of a linear relationship. Question 1 Covariance and Correlation The table below shows a set of sample bivariate data. Calculate the covariance and correlation coefficient by completing the below table. Show all working. X Y (X - X) ( Y - Y ) (X - X ) ( Y - Y) 3 0 1 3 5 6 6 9 5 7 Note: To compute sample means and sample standard deviations, you can use Excel or a calculator; no working is required. (2 marks)Online Problems 7 Coverage: Sec. 4.11, 5.1, 5.2, 5.4 E Question 9 --/10 View Policies Current Attempt in Progress Determine the covariance and correlation for the following joint probability distribution. Round your answers to four decimal places (e.g. 98.7654). X -1 -0.5 0.5 1 -7-1 1 2 fxr (x, )) 1/8 1/4 1/2 1/8 Covariance = i Correlation = i Statistical Tables and Charts e Textbook and Media Save for Later