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Binomial and Geometric Probability Distribution (and the calculator) 1. Each child born to a specific set of parents has probability of 0.25 of having blood type O blood. Then X is B(5, .25). a. Verify that X meets the setting requirements for a binomial distribution. b. Make a table for the pdf of the random variable X. Then use the calculator to find the probabilities of all possible values of X and complete the table. c. Verify that the sum of the probabilities is 1. d. Construct a histogram of the pdf on paper. e. Use the calculator to find the cumulative probabilities and add these values to your pdf table. Now construct a cumulative distribution histogram on paper. f. Use your work to answer the following questions: i. What is the probability that exactly 2 of the children have type O blood? ii. What is the probability that at least 3 of the 5 children have type O blood? 2. An experiment consists of rolling a die until a 3 occurs. Let X= number of rolls required to get the first 3. Then G(1/6,n). a. Verify that X meets the setting requirements for a geometric distribution. b. Construct a probability distribution function (pdf) to include at least 5 entries for the probabilities X. Record the probabilities in a table to four decimal places. c. Construct a histogram of the pdf on paper. d. Compute the cumulative distribution function and make its histogram e. What is the probability of getting the first success on i. The third roll? ii. On the fourth roll? The Mean and standard deviation of the Binomial random variable 1. Return to problem 1 above. What is the mean and standard deviation for the binomial situation B(5, .25)? Hint: Create lists in the statistics editor ( ( L1 , L2 ) and then use the capabilities of your calculator to find the mean and standard deviation. 2. Make a generalization (in terms of a formula as to how to find the mean for a binomial distribution. 3. If possible, make a generalization as to how to find the standard deviation of the binomial distribution.