Concept explainers
Consider a random sample of size n from a continuous distribution having
W =1 Y1 + Y2 + 3. Y3 +….+ n Yn =
where the Yi’s are independent Bernoulli rv’s, each with p = .5 (Yi = 1 corresponds to the observation with rank i being positive).
a. Determine E(Yi) and then E(W) using the equation for W. [Hint: The first n positive integers sum to n(n + 1)/2.]
b. Determine V(Yi) and then V(W). [Hint: The sum of the squares of the first n positive integers can be expressed as n(n + 1)(2n + 1)/6.]
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Chapter 5 Solutions
Probability and Statistics for Engineering and the Sciences
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