(10 points) Suppose there are two student assistants working as typists in the m
ID: 3075170 • Letter: #
Question
(10 points) Suppose there are two student assistants working as typists in the main office of the Statistics & Applied Probability Department at UCSB. The number of typos per page made by student assistant A is a Poisson random variable with parameter XA-1. The number of typos per page made by student assistant B is also a Poisson random variable with an average of 10 typos per page. One of the professors in the department asks one of the students to type up a letter. From experience, this work will be done with 1/3 probability by student A and with 2/3 probabilit,y by student B (a) What is the probability that the typewritten letter will contain exactly one typo? (b) It turns out that the typewritten letter does not contain any typos. Given this informa- tion, what is the probability that student B typewrote this letter?Explanation / Answer
a)P(exactly one typo)=P(student A and exactly one typo)+P(student B and exactly one typo)
=(1/3)*(e-1*11/1!)+(2/3)*(e-10*101/1!) =0.1229
v)
P(no typos)=P(student A and no typo)+P(student B and no typo)
=(1/3)*(e-1*10/0!)+(2/3)*(e-10*100/0!) =0.1227
P(student B |no typos)=P(student B and no typo)/P(no typos)=(2/3)*(e-10*100/0!)/0.1227=0.000247
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