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Q 1.An online retailer, Mr Collins Ndhlovu, has two adverts posted in different parts of a...

Q 1.An online retailer, Mr Collins Ndhlovu, has two adverts posted in different parts of a well-known social networking website, Advertisement A and Advertisement B. An average of 2 ‘clicks’ are generated by Advertisement A during the period Monday 10.00 to 10.05am. There are on average 5 ‘clicks’ generated by Advertisement B during the same period. Calculate the probability that on a particular Monday between 10.00 and 10.05 am: i)Advertisement A generates at most 3 clicks. ii)Advertisement A generates at least 4 clicks. ii)Advertisement B generates no more than 4 clicks. iv)Advertisement A generates exactly 2 clicks and Advertisement B exactly 2 clicks. v)At least 3 clicks are generated in total by the two advertisements. (5marks)

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Expert Solution

Let X is a random variable shows the number of clicks on Advertisement A. Here X has Poisson distribution with parameter . The pdf of X is

Let Y is a random variable shows the number of clicks on Advertisement B. Here Y has Poisson distribution with parameter . The pdf of Y is

(i)

​The probability that on a particular Monday between 10.00 and 10.05 am advertisement A generates at most 3 is

(ii)

​The probability that on a particular Monday between 10.00 and 10.05 am advertisement A generates at least 4 clicks is

(iii)

​The probability that on a particular Monday between 10.00 and 10.05 am advertisement B generates no more than 4 clicks is

(iv)

​The probability that on a particular Monday between 10.00 and 10.05 am advertisement A generates exactly 2 clicks is

​The probability that on a particular Monday between 10.00 and 10.05 am advertisement B generates exactly 2 clicks is

The probability that on a particular Monday between 10.00 and 10.05 am advertisement A generates exactly 2 clicks and Advertisement B exactly 2 clicks is

(V)

Let Z = X+Y

The distribution of Z will be Poisson distribution with parameter . The required probability is:

milcah answered 4 months ago
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