Probability and statistics assignment.

Problem 5. [1 point per question.] Suppose we have some data (21 , y1), (72, 32), (ra, y, ) given by (0, 0), (1, 1), (2,3). In the questions below, show how you are using a formula and end up giving your answer in numerical form; part (a) is shown as an example. Consult the Useful Formulas sheet as needed. a) Find 7. Solution: 7 = Dtete - 0112 = ] 41. Consider 3 students who wear similar-looking black coats to a party. When they leave the party, they are in a hurry, and they each randomly grab a coat as they depart, with all possibilities equally likely. Use inclusion-exclusion to calculate the probably that none of them get their correct coat. [Hint: First find the probability that at least one of them gets their correct coat.] Grade this question? Yes No 2. Suppose that X and Y are independent random variables, such that X has probability mass function px(r) = (1/3)(2/3)*-1 for integers r 2 1, and Y' has probability mass function py(y) = (3/4)(1/4)"- for integers y 2 1. 2a. What kind of variables are X and Y? What are their parameters? 2b. What is Var (X - Y)? 2c. Find the probability that X and Y are equal.Problem 2. [6pts] All the 143 Android phone visits to the web site math. hawaii. edu last month were done using either the default web browser or the Opera Mini browser. . Four visits used Opera Mini. 1 of these 4 was a new visit (the other three being returning visits). . 139 visits used the default browser. 30 of these were new visits. a) [3 points] How many percent of all visits using Android phones were new visits? b) [3 points] What percentage of new visits used the default browser?Problem 3. Suppose that houses in La Jolla area are sold at a rate of 1.02 per day, and that on average, 13.3% of the houses sold are built in the first half of 1963 or earlier (we will call such houses "old" ). Real estate agent Sally has noticed that the numbers of houses, old and new, and the numbers of buyers and sellers in the market, are very large compared to the number of sales that typically occur in a month. Therefore she adopts the following mathematical modeling assumptions: Ages of houses sold are independent of one another, and the number of sales, and the time until the next sale, are independent across time periods. Based on these assumptions answer (a)-(d) below. a) [3 points] Find the probability that exactly 1 of the next 7 houses sold will be "old". b) [3 points] Find the probability that exactly 8 houses will be sold in the next (7-day) week. c) [2 points] What is the probability that it will be at least a 7-day week (from now) before the next house is sold? d) [2 points] Suppose no houses are sold in April. What is the probability that no house will be sold in the first 7-day week of May?Problem 1. 5 points] Suppose a store sells boxes of cream puffs. Each box contains 12 cream puffs, and each cream puff is either chocolate cream or vanilla cream. The number of chocolate cream puffs in a box has a mean of 4 and a standard deviation of 2.6. If you buy 7 boxes of cream puffs, what is the standard deviation of the number of vanilla cream puffs that you will get? You may assume that the numbers of vanilla cream puffs in different boxes are independent of one another.Let Aj =event that the first ball is blue, and Az= event that second ball is blue. P(A)) = 0.4, P(A:|Aj) = 3/9, P(A, n A2) = P(A]) P(AJA]) = 4/30 = 0.133. 6. Consider a family photo where the grandmother is to be in the center of a line of people. Given 7 family members in the photo (including grandmother), how many different ways are there to line up the people?5. Roll five (6-sided) dice. Let D be the event that the sum of the values on the five dice is exactly 8. Let A be the event that exactly 4 of the 5 dice have the value "1". Let / be the event that exactly 3 of the 5 dice have the value "1". Let C be the event that exactly 2 of the 5 dice have the value "1". 5a. Find P(A | D). 5b. Find P( B [ D). 5c. Find P(C | D). [Hint: Given that event D occurs, we know that A or B or C occurs, and these three events are disjoint, so we should have P(A | D) + P(B | D) + P(C | D) - 1.]X - H 45 - 40 Z = ~ N(0,1), = 2.273 2.2 From a standard normal table, P(z > 2.273) = 1 - P(z