Question

(Section: Joint distributions)

1) Suppose that Kirie goes to a bowling alley to plays some game. In one of those games played, her scored follows a pattern of normal distribution by an average of one hundred and forty with a standard deviation of twenty. She has played for two games in the roll, and scores in each game had the same probability distribution. Let A and B be random variables, and C = A + B be her scores of two games combined.

(a) For her combined scores for two games, what are the standard deviation and the mean? (Assumed her two scores of A and B are independent.)

(b) Suppose that the correlation coefficient scores in each game are 0.6. What would the probability of her combined scores if to reached over three hundred?

(c) Using the same correlation coefficient. How would it affect the given standard deviation and the mean? Would it affect her combined scores as well?

(d) Without the previously given coefficient. What would then be the probability of her two combined scores if to reached over three hundred?

(e) Using questions (b) and (d) with a positive correlation, how does it compare between the two, and why does it make sense? (Assume both answers are independent.)

Answer 1