Starting at a fixed time, we observe the gender of each newborn child at a certain hospital until a boy (b) is born. assume that successive births are independent and let y = the number of girls born before the experiment terminates. with p = p(b)and 1 − p = p(g), what is the pmf of y? [hint: first list the possible values of y, starting with the smallest, and proceed until you see a general formula.] (enter your answer in terms of p and y.)

p(y) = y = 0, 1, 2, 3, 4,

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?