TQ5 Please help

Let X be the number that comes up on a fair 6-sided die. What is E[X] and Var(X) ? Let I be a random variable which takes value 1 when the die value is greater than 3 and I equals 0 otherwise. What is E[I] and Var(!) ? Now suppose we throw 10 dice. Let X, be the result for ith die. What is E[X1+X2+...+X10] ? A computer program crashes at the end of each hour with probability p, if has not done so already. What is the expected time until the program crashes ? Express in terms of p. Useful fact: ), ixl- =7. Write a Matlab simulation and compare its estimate with your calculation. The time to run a cloud computing task is X = 1/N + Y, where N is the number of servers allocated to the task and Y is a random variable with E[Y]=0. Suppose n=2 servers are allocated, what is E[XIN=2] ? Suppose the number of available servers has PMF: P(N=1)=0.5, P(N=2)=0.2, P(N=3)=0.2, P(N=4)=0.1. What is E[X] ? Suppose the number of people using a mobile app in a day is a random variable N with PMF P(N=n) =_ 1-1/2 On average each person pays E1 per day to use the service. What is the expected revenue for this app ? Useful fact: Epix' = (1-x)2 A tout is buying tickets for a concert. The price of the tickets is 650 and the tout sells them for 6100, making a profit of 650. However, if he can't sell a ticket then he makes nothing from it (so it costs him (50). Let random variable N be the number of people who will buy tickets from the tout. N has PMF P(N=n)= (1 - e=0.5)e-0.5m. Suppose the tout buys m=10 tickets, what is his expected profit or loss ? Express in terms of m, n and constants. Using Matlab plot the expected profit vs m. What value of m maximizes profit ?Let X be the number that comes up on a fair 6-sided die. What is E[X] and Var(X) ? Let I be a random variable which takes value 1 when the die value is greater than 3 and I equals 0 otherwise. What is E and Var(!) ? Now suppose we throw 10 dice. Let Xi be the result for ith die. What is E[X1+X2+...+X10] ? A computer program crashes at the end of each hour with probability p, if has not done so already. What is the expected time until the program crashes ? Express in terms of p. Useful fact: >in ix = guns. Write a Matlab simulation and compare its estimate with your calculation. The time to run a cloud computing task is X = 1/N + Y, where N is the number of servers allocated to the task and Y is a random variable with E[Y]=0. Suppose n=2 servers are allocated, what is E[XIN=2] ? Suppose the number of available servers has PMF: P(N=1)=0.5, P(N=2)=0.2, P(N=3)=0.2, P(N=4)=0.1. What is E[X] ? Suppose the number of people using a mobile app in a day is a random variable N with PMF P(N=n) =. On average each person pays E1 per day to use the service. What is the expected revenue for this app ? Useful fact: Epix' = (1-x)i A tout is buying tickets for a concert. The price of the tickets is 650 and the tout sells them for (100, making a profit of 650. However, if he can't sell a ticket then he makes nothing from it (so it costs him (50). Let random variable N be the number of people who will buy tickets from the tout. N has PMF P(N=n)= (1 -e-0.5)e-0.5n. Suppose the tout buys m=10 tickets, what is his expected profit or loss ? Express in terms of m, n and constants. Using Matlab plot the expected profit vs m. What value of m maximizes profit