Question

An Internet service provider company has installed a modem to serve the needs of 1 customer in an arbitrary region Suppose that once a connection service is requested by a customer, one unassigned modem must be immediately assigned to the customer or the request will be denied At each time period, a customer may request for a connection service with a probability of 0.7 a. What is the probability distribution of a customer request for a connection? It suffices to write the exact formula. b. Use Excel to generate 10 random numbers for customer requests with Bernoull distribution with parameter p 0.65 (please aso add the screenshot of Excel in your answer sheet) Question 2(10.10 20 points) Consider the following systemm with 15 identical components. As you may guess, this system is functional provided that every single component is working. Hence, once one of the component is broken, the system stops working. Each of the components is assumed to independently work with a probability of 0.8 over a day 13 a. What is the probability that this system works the whole day? b. Now use Excel to compute the probability formula that you provided to part (a). Question 3(6 +6+6+6+6 30 points) Two dices are rolled at the same time and the squared difference between their top faces is What is the probability that the squared difference of the top faces is 0? What is the probability that the squared difference of the top faces is 17 In general, how can we calculate the probabilities for all possible values of the squared difference of the top faces in Excel? a. b. c. d. Compute the Cumulative Empirical Distribution (CDF) for part c e. Plot column charts for both probability (PDF) and COF Question 4 (S+5+5+5-20 points) For each of the parts (a) through (d), write a syntax in Excel a. Generate a real number in the range [o,15). b. Generate a real number in the range [11,19 c. Generate an integer number in the inclusive range from 1 to 10 d. Generate a fractional number with its integer nominator extracted randomly in the inclusive range 1 to 2 and its integer denominator extracted randomly in the inclusive range 1 to4 Question S (10 points) Using Excel calculate the matrix multiplication. (Hint: use MMULT(arrayl,array2) ay23

Answer 1

Given that n , the tota numbe Since. p- o.s0 P 0.65

o0258 000 0 SES 00a 5123 1 2 s13 oo4 8 21265 02 6o 24250 0-09493 foto o.2485 o 441/ 0.461 d. 23 5S6 2 0t2 6 TRU INOMDsr (A 5 a, a As 1o, 0.65 TRUE 0.6 DİST