aug15p - EXAM P QUESTIONS OF THE WEEK S. Broverman, 2005...

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EXAM P QUESTIONS OF THE WEEK S. Broverman, 2005 Question 4 - Week of August 15 A random variable has a probability mass of 0.2 at and a probability mass of 0.1 at \\ œ ! \œ" \ . For all other values, has the following density function: , where is a constant. B Ñœ - !B ! B !B" #B "  B  -   - \ H (a) Find Þ&\"Ñ (b) Find TÐ\" l\Þ&Ñ (c) Find the mean of . \ The solution can be found below.
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Question 4 Solution (a) Þ&\"Ñœ B.B œ Þ$(&Þ ' Þ& " (b) . TÐ\" l\Þ&Ñœ TÐÞ&\"Ñ TÐ\Þ&Ñ From part (a), the numerator is . Þ$(& Although we have not determined the value of , we know that - TÐ\  Þ&Ñ œ "  TÐ\ Ÿ Þ&Ñ œ "  ÒTÐ\ œ !Ñ  TÐ!  \  Ÿ Þ&ÑÓ œ "  ÒÞ#  B .BÓ œ "  Þ$#& œ Þ'(& Þ ' ! Þ& Then . TÐ\  "l\  Þ&Ñ œ œ œ Þ&&' TÐÞ&\"Ñ TÐ\Þ&Ñ Þ'(& Þ$(& (c) In order for to be a properly defined random variable, total probability over the probability
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aug15p - EXAM P QUESTIONS OF THE WEEK S. Broverman, 2005...

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