Please provide solutions to the following question. Thank you. 3) A manuscript i

Question

Please provide solutions to the following question. Thank you.

3) A manuscript is sent to a typing firm consisting of typists A,B and C. If it is typed by A then the number of errors is a Poisson random variable with mean 2.6; if it is typed by B then the number of errors is a Poisson random variable with mean 3; if it is typed by C then the number of errors is a Poisson random variable with mean 3.4. Let X denote the number of errors in the typed manuscript. a) Assume that one typist is randomly selected to do all the work. Find the mean and variance of X b) Assume instead that the work is divided into three equal parts which are given to the three typists. Find the mean and variance of X in this case.

Explanation / Answer

we have to select one typists randomaly from A, B and C we use simple random sampling without replacement scheme.

By this scheme suppose we select C typists then we know that poisson random variable have same mean and variance.

Therefore mean = Variance = 3.4

b)

We use additive proparty of poisson random variable i. e. Let Z = A + B + C then Z follows poisson distribution with mean 2.6 + 3 + 3.4 = 9.

Mean = Variance = 9

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