GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY.

Hi,kindly reply with whole answers correct,accurate answers and step by step working.Do not skip step.Be very clear and mention about the formula for each step.Make sure the answers are correct and accurate. Be very organised with the working and systematic.Please explain to support and make it clear.

STA108

DECEMBER 2019

QUESTION 5 a) A manager is dividing her staffs randomly into groups for a charity project. There will be four staff in a group. In the company, there is a total of 32 staff, in which 12 are female. Find the probability that a group has equal number of male and female staff. (3 marks) b) Determine the number of ways to form seven-letter word from the letters R, M, N, M M, U and A if repetition is not allowed and the letter R must be in the middle (3 marks) c) The events A and B are such that P(A UB) = _ and P(A) = =. Find P(AnB). (3 marks) QUESTION 6 Tania has three options to go to work where she can drive her own car, take the train or grab car. The probability that she will choose each option is 40%, 50% and 10%, respectively. If she drives her own car to work, there is 45% chance of arriving late at her workplace and only 30% if she took the train. However, if she uses the grab car, the probability she will arrive on time is 75%. a) Draw a tree diagram for the above situation. (3 marks) b) Calculate the probability that Tania will on time at her workplace. (2 marks) c) Given that in a particular day she was late, find the probability that she took a grab car on that day. (3 marks)QUESTION 7 A random variable Y has a discrete probability distribution given in the following table. Y = y -1 0 1 P(Y = y) S a) Given that E(Y) =- and E(Y?) = >, find the values of q, r and s. (7 marks) b) Calculate P(Y 2 0). (2 marks) c) Calculate E(-5 - 5Y + 3Y2). (2 marks) QUESTION 8 Suppose that Y is a continuous random variable that represents the customers' waiting time (in minutes) after ordering bubble milk tea at ChatTea Cafe. The probability density function is given as follows: f(y) =6 (0.5+y) for 0sys3 10 for elsewhere a) Compute the probability of a customer that has to wait for at most 2 minutes. (3 marks) b) Calculate the expected waiting time of customers to receive their order. (4 marks) c) Calculate the variance waiting time of customers to receive their order. (5 marks) d) Compute V(2Y + 3). (2 marks)