5. Consider a trinary communication channel [STAR 1979] whose channel diagram is shown in Figure 1.P.6. For i = 1,2,3 let T, denote the event "digit i is trans mitted" and let R₂ denote the event "digit i is received." Assume that a 3 i transmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1 If a 1 has been received, what is the expression for the probability that a 1 wa sent? Derive an expression for the probability of a transmission error. P(R171) =1-α R1 T1% a/2 α/2 B/2 1-ẞ R2 T29 ẞ/2 Y/2 Y/2 T3 1-y R3 Figure 1.P.6. A trinary communication channel: channel diagram

8. Let A, B be two events with P(A) = ½, P(A − B) = 3, determine P(AB).

Cynthia is president of an international chemical distribution company, Cchem. Weekly gross sales for Cchem has a mean of $1 million and standard deviation of $0.2 million; the distribution of sales is highly right-skewed. One week’s sales are independent of the sales in any other week. Use this information to answer questions 5 to 6 below. What is the probability that sales for the week of October 5, 2009 will be more than $1.25 million? In order for Cynthia to receive a bonus, Cchem’s annual sales must exceed $53 million. What is the probability that Cynthia will receive a bonus for the fiscal year starting in 2010? Assume there are 52 weeks in a year.

What would be the correct way of doing this?