Please type the answer here, not on a paper please and thank you. Q1/

Compute the mean and variance of the following discrete probability distribution. x Pix) 2 .5 8 .3 10 .2 The information below is the number of daily emergency service calls made by the volunteer ambulance service ofWaIterboro, South Carolina, for the last 50 days. To explain, there were 22 days on which there were two emergency calls, and 9 days on which there were three emergency calls. Number of Calls Frequency 0 8 1 10 2 22 3 9 4 1 Total 50 The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experi- ence. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions. Admissions Probability 1,000 .6 1,200 .3 1,500 .1 Levinson's Department Store is having a special sale this weekend. Customers charging purchases of more than $50 to their store credit card will be given a spe- cial Levinson's Lottery card. The customer will scratch off the card, which will indi- cate the amount to be taken off the total amount of the purchase. Listed below are the amount of the prize and the percent of the time that amount will be deducted from the total amount ofthe purchase. Prize Amount Probability $ 10 .50 25 .40 50 .08 100 .02 . In a binomial situation, n = 4 and it = .25. Determine the probabilities of the follow- ing events using the binomial formula. a. x = 2 b. x = 3 Assume a binomial distribution where n = 5 and 1: = .30. a. Refer to Appendix 3.1 and list the probabilities for values ofx from 0 to 5. b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (61) and (62)