Alice, Bob, and Carl arrange to meet for lunch on a certain day. They arriveindependently at uniformly distributed times between 1 pm and 1:30 pm on that day. Required:
a. What is the probability that Carl arrives first?
b. What is the probability that Carl will have to wait more than 10 minutes for one of the others to show up?
c. What is the probability that Carl will have to wait more than 10 minutes for both of the others to show up?
d. What is the probability that the person who arrives second will have to wait more than 5 minutes for the third person to show up?

(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?

What is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)? y=-3x-5 o y=3x-5 y=-3x+5 0y=3x+5

The discrete random variables x and y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 tabulate the distribution and show that a = 0.1.2 find the marginal distributions of x and y. 3 calculate cov(x,y).4 state, giving a reason, whether x and y are independent. 5 calculate e(y|x = 1).