Example Class 7 - The University of Hong Kong Department of Statistics and Actuarial Science STAT1801 Probability and Statistics Foundations of

# Example Class 7 - The University of Hong Kong Department of...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT1801 Probability and Statistics: Foundations of Actuarial Science (10-11) Example Class 7 1.Let 𝑋𝑋be the number of bad records in each 100 feet of a used computer tape. Assume 𝑋𝑋follows a Poisson distribution with mean 4. Let 𝑊𝑊be the number of feet before the first bad record is found. a)Find the distribution, mean and variance of 𝑊𝑊b)Find 𝑃𝑃(𝑊𝑊 ≤20)and 𝑃𝑃(𝑊𝑊> 60|𝑊𝑊> 20)c)Let 𝑍𝑍be the number of feet before the third bad record is encountered. i)Find the distribution, mean and variance of 𝑍𝑍ii)Find 𝑃𝑃(𝑍𝑍 ≤100)2.Suppose 𝑋𝑋and 𝑌𝑌have the joint density function 𝑓𝑓(𝑥𝑥,𝑦𝑦) =1𝑥𝑥2𝑦𝑦2,𝑥𝑥> 1,𝑦𝑦> 10, otherwisea)Find the joint density function of
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