# 410Hw02 - STAT 410 Summer 2009 Homework #2 (due Wednesday,...

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STAT 410 Summer 2009 Homework #2 (due Wednesday, June 24, by 4:00 p.m.) 1. The time, T, that a manufacturing system is out of operation has cumulative distribution function F ( t ) = - otherwise 0 2 if 2 1 2 t t The resulting cost to the company is Y = T 2 . Determine the density function of Y. 2. Grades on the last STAT 410 exam were not very good. Graphed, their distribution had a shape similar to the p.d.f. f X ( x ) = 000 , 5 1 ( 100 – x ), 0 x 100, zero elsewhere. a) What was the class average, E ( X ) ? As a way of “curving” the results, the professor announces that he will replace each person’s grade, X, with a new grade, Y = g ( X ), where g ( X ) = 10 X . b) Find the p.d.f. that describes the new grades, Y. c) Has the professor’s strategy been successful in raising the class average above 60? What is the new class average, E ( Y ) ?

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3. Suppose that X follows a uniform distribution on the interval [ π / 2 , π / 2 ] .
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## This note was uploaded on 10/29/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

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410Hw02 - STAT 410 Summer 2009 Homework #2 (due Wednesday,...

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