Question
In Kerrich's urn experiment, suppose you get $1 for each red ball and $0 for each green one, and let X and Y represent the
In Kerrich's urn experiment, suppose you get $1 for each red ball and $0 for each green one, and let X and Y represent the dollars you receive on the two draws within a single trial of the experiment. Exercise 1.34. Write down the probability distribution of X and Y in tabular form. Your table should have columns for X, for Y , and for the joint probability of X and Y , i.e. Pr[X, Y ]. Exercise 1.35. What are the expected values of X and of Y ? Exercise 1.36. What are the variances of X and of Y ? Exercise 1.37. What is the covariance of X and Y ?
I did 1.34, but I'm confused on how I can apply what I did to the other exercises. Here is my answer for 1.34:
X (first draw) | Y (second draw) | Pr[X,Y] | Event |
1 | 1 | 1/6 | RR (two red balls) |
1 | 0 | 1/3 | RG (red ball then green ball) |
0 | 1 | 1/3 | GR |
0 | 0 | 1/6 | GG |
I'm probably overthinking this but whatever help you can provide would be great thank you!
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