Group - 9 questions QUESTION 2.1 Consider an experiment of tossing 3 fair coins and counting the number of heads. List all the possible values that X {random variable representing the number of heads} can take on and the probability that corresponds to the X values provided. Response - 5 points III-Illll Your response... 0 words A program consists of two modules. The number of errors X1 in the first module has the pmf P1(x), and the number of errors X2 in the second module has the pmf P2(x), independently of X1, where X P1(x) P2(x) 0 0.6 0.7 0.25 0.25 NJ 0.03 0.05 0.12 Find the pmf and cdf of Y = X1 + X2, the total number of errors.QUESTION 2.3 As part of a business strategy, randomly selected 22% of new internet service subscribers receive a special promotion from the provider. A group of 10 neighbors signs for the service. What is the probability that at least 3 of them get a special promotion? (Hint: Review Example 3.16) Response . 5 points B U Your response... 0 words ATTACH FILE(S) DRAG & DROP Max size 4.0 GB SAVE QUESTION 2.4 An exciting computer game is released. Fifty-five percent of players complete all the levels. Thirty percent of them will then buy an advanced version of the game. Among 20 users, what is the expected number of people who will buy the advanced version? What is the probability that at least two people will buy it? (Hint: Review Example 3.17) Response . 5 pointsQUESTION 2.5 Customers of an internet service provider initiate new accounts at the average rate of 15 accounts per day. (a) What is the probability that more than 10 new accounts will be initiated today? (b) What is the probability that more than 16 accounts will be initiated within 2 days? (Hint: Review Example 3.22) Response . 8 points B 1 U E Your response... 0 words ATTACH FILE(S) DRAG & DROP Max size 4.0 GB SAVE QUESTION 2.6 Ninety-seven percent of electronic messages are transmitted with no error. What is the probability that out of 200 messages, at least 150 will be transmitted correctly? (Hint: Review Example 3.24) Response . 5 pointsQUESTION 2.7 A and B are two competing companies. An investor decides whether to buy a. 100 shares of A, or b. 100 shares of B, or c. 50 shares of A and 50 shares of B. A profit made on 1 share of A is a random variable X with the distribution P(X = 2) = P(X = -2) = 0.5. A profit made on 1 share of B is a random variable Y with the distribution P(Y = 4) = 0.2, P(Y = -1) = 0.8. If X and Y are independent, compute the expected value and variance of the total profit for strategies (a), (b), and (C).QUESTION 2.8 A disk has free space of 330 megabytes. Is it likely to be sufficient for 400 independent images, if each image has expected size of 1 megabyte with a standard deviation of 0.6 megabytes? (Hint: Review Example 4.13; Remember to show all work to justify your answer) Response . 7 points B U S Your response... 0 words ATTACH FILE(S) DRAG & DROP Max size 4.0 GB SAVE QUESTION 2.9 You wait for an elevator; whose capacity is 2000 pounds. The elevator comes with ten adult passengers. Suppose your own weight is 175 lbs, and you heard that human weights are normally distributed with the mean of 165 Ibs and the standard deviation of 20 lbs. Would you board this elevator or wait for the next one? Provide an argument by determining whether or not overload is likely. (Hint: Review Example 4.14; Remember to show all work to justify your answer) Response . 7 points