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hw20 - 5 • the value of g X 1 ·· g X n/n is...

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ENEE 324 ASSIGNMENT 20 Due Tue 11/24 Let X 1 ,X 2 ,X 3 ,... be independent positive random variables with pdf as shown below, where 0 < b < a . 0 a - b a a + b x f X ( x ) ? The sequence is recorded using an instrument with dynamic range [0 , 5]. Thus the recorded values g ( X i ) are such that g ( X i ) = X i whenever X i 5, and g ( X i ) = 5 if X i > 5. It is found that for a large sample size n , the relative frequency of recorded values g ( X i ) = 5 is approximately equal to 12
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Unformatted text preview: . 5%; • the value of ( g ( X 1 ) + ··· + g ( X n )) /n is approximately 3.96. (i) (14 pts.) What are your estimates of a and b based on the given information? Explain your answer. (ii) (6 pts.) What is the likely value of the relative frequency of g ( X i )’s (where 1 ≤ i ≤ n ) which are less than 3.00? Explain your answer....
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