Winston the labradoodle loves to play fetch. He catches his ball mid-air with probability p and catch attempts are statistically independent of one another. Winston attempts to catch his ball in a series of five tosses and then he takes a water break. The data set labeled ”Winston” reports the number of catches over 3,500 trials of five tosses each. (a) Define a random variable Y equal to the number of times Winston catches the ball mid-air in a series of five tosses. How many possible outcomes of Y are there? Report your answer as an integer. (b) What proportion of the time did Winston catch exactly two balls mid-air out of five tosses? Round your answer to three decimal places. (c) What proportion of the time did Winston catch exactly three balls mid-air out of five tosses? Round your answer to three decimal places. (d) Use the data to estimate p, the probability that Winston catches each ball where: p = Total Catches Total Catch Attempts. Round your answer to three decimal places. Use your estimate of p above to compute the PDF of Y assuming Y is a binomial random variable. (e) Report P(Y = 0). Round your answer to three decimal places. (f) Report P(Y = 1). Round your answer to three decimal places. (g) Report P(Y = 2). Round your answer to three decimal places. (h) Report P(Y = 3). Round your answer to three decimal places.
Winston the labradoodle loves to play fetch. He catches his ball mid-air with probability p and catch attempts are statistically independent of one another. Winston attempts to catch his ball in a series of five tosses and then he takes a water break. The data set labeled ”Winston” reports the number of catches over 3,500 trials of five tosses each.
(a) Define a random variable Y equal to the number of times Winston catches the ball mid-air in a series of five tosses. How many possible outcomes of Y are there? Report your answer as an integer.
(b) What proportion of the time did Winston catch exactly two balls mid-air out of five tosses? Round your answer to three decimal places.
(c) What proportion of the time did Winston catch exactly three balls mid-air out of five tosses? Round your answer to three decimal places.
(d) Use the data to estimate p, the probability that Winston catches each ball where: p = Total Catches Total Catch Attempts. Round your answer to three decimal places. Use your estimate of p above to compute the
(e) Report P(Y = 0). Round your answer to three decimal places.
(f) Report P(Y = 1). Round your answer to three decimal places.
(g) Report P(Y = 2). Round your answer to three decimal places.
(h) Report P(Y = 3). Round your answer to three decimal places.
(i) Report P(Y = 4). Round your answer to three decimal places.
(j) Report P(Y = 5). Round your answer to three decimal places.
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