A manuscript is sent to a typing unit to be typed by one of three typists, Typist 1, Typist 2 or Typist 3. The probability distribution of the number of errors for Typist j is Poison with mean parameter λj ; for j = 1, 2, 3. Assume that each of the three typists is equally likely to be asked to do this typing job and let V denote the number of typing errors that are present in the completed job.

(b) Suppose that there are n typing errors, i.e. V = n. Calculate the probabilities P[Typist j did the typing|N = n],j=1,2,3.

(c)Suppose that λ1 < λ2 < λ3. If N = 0, which typist is most likely to have done the typing? Give justifification.

(d) Still assuming λ1 < λ2 < λ3, which typist is most likely to have done the typing if N is large? What is the probability that the most likely typist in fact did the typing? What is the limiting value of this probability as n → ∞? Show your calculations.

Please carefully read the questions then answer part b to part d