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### dec26p

Course: STATISTICS 50, Spring 2010
School: California State...
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Word Count: 357

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P EXAM QUESTIONS OF THE WEEK S. Broverman, 2005 Week of December 26/05 The random variable \ is defined on the interval ! # . You are given T \ &quot; &quot; , J Bl\ &quot; B# , J Bl\ &quot; B &quot; , I\ &quot; . % Find J &quot; . The solution can be found below. Week of December 26 - Solution Let T \ &quot; - For B &quot;, J Bl\ &quot; J B T...

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P EXAM QUESTIONS OF THE WEEK S. Broverman, 2005 Week of December 26/05 The random variable \ is defined on the interval ! # . You are given T \ " " , J Bl\ " B# , J Bl\ " B " , I\ " . % Find J " . The solution can be found below. Week of December 26 - Solution Let T \ " - For B ", J Bl\ " J B T \" J B - B# , so that J B -B# for ! B " . \$ % J " T \ " T \ " - For " B # , J Bl\ " " % , so T \ " " J " J B- " % \$ % - - . J BJ " T \" " % B", so that for " B # , J B - \$ -B " . % Then % \$ WB " J B is equal to " -B# for ! B " , W" and WB " - # " % - , \$ -B " \$ -# B for " B # . % % " # I\ '! WB .B '! " -B# .B '" \$ -# B .B % " \$ \$ - " % # * #! T \ " - so that \$\$#!" #% * J " #! " % p- "% #! * #! . . Note that we have used the expectation rule for a non-negative random variable \ , I\ '! WB .B ; since \ is defined on ! # we have J B " for B # and W# ! for B # . Also note that since \ has a discrete point of probability at B ", the " # integral of WB can be split into '! and '" .
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California State University, Monterey Bay - STATISTICS - 50
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