Question 22 Let X equal the number of bits in error in the next four bits transmitted. The possible values for X are {0, 1, 2, 3, 4} Suppose that the probabilities are points Save Alls P(x =0)-0.45 P(x=1)-D0.19 P(x 2)-0.15 P(x=3)3D0.10 P(x-4)3D0.10 Find E(X) Oa 1.19 Ob 0.35 Oc 22 Od o

For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forced to wait in queue is an important measure of performance of the M/M/N/∞ system. This probability is given by PQ N!(1 – p/N) | and is known as the Erlang C formula. Please derive the equation. What is the expected number of customers waiting in the queue (not in service)?

Please explain further the solution. Thank you!

(-1)" Σ n=2

Question 5. A professor decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 400 students in his course the same final exam, but some students have 90 minutes to complete the exam while others have 120 minutes. Each students is randomly assigned one of the examination times based on the flip of a coin. Let Y, denote the number of points scored on the exam by the ith student (0 ≤ Y ≤ 100), let X, denote the amount of time that the student has to complete the exam (X, = 90 or 120), and consider the regression model Yi = Bo + BiXitu. (1) Explain what the term u, represents. Why will different students have different values of ui? (2) Explain why E(u₁|X₁) = 0 for this regression model. (3) The Least Squares Assumptions Yi Bo + B₁Xi + Ui, i = 1,..., n, where I The error term u, has conditional mean zero given X₂: E(ui Xi) = 0; II (X₁, Yi), i 1,, n, are independent and identically distributed (i.i.d.) draws from their joint…

Consider the following scenario: • Let P(C) = 0.3• Let P(D) = 0.8• Let P(C|D) = 0.3 A. P(C AND D) = [ Select ]  ["0.30", "0.24", "0.26", "0.11"]            B. Are C and D Mutually Exclusive? [ Select ]  ["No, they are not Mutually Exclusive.", "Yes, they are Mutually Exclusive."]            C. Are C and D independent events?[ Select ]["No, they are Dependent.", "Yes, they are Independent."]            D. P(C OR D) = [ Select ] ["0.92", "0.86", "0.60", "1.1"]            E. P(D|C) = [ Select ]["0.30", "0.95", "0.24", "0.80"]