Unformatted text preview: number of signals the machine receives. Let the number of positive signals it receives be η and ﬁnd the distribution of η . 4. Put n balls randomly into m boxes, ξ is the number of empty boxes. Calculate E [ ξ ]. 5. Ross Page 195, problem 65 6. Ross Page 200, problem 27 7. The Pareto distribution, with parameters α and β , has probability density function f ( x ) = α β β x β +1 ,α < x < ∞ ,α > ,β > a) Verify that f ( x ) is a probability density function b) Derive the mean and variance, and specify the conditions we must impose on β in order for the mean and variance to be ﬁnite. 8. Random variable X has a probability density f ( x ) = 1 2 x + 3 4 , ≤ x ≤ 1 and f ( x ) = 0 elsewhere. Calculate P ((  2 X 335 216  > 19 216 ) ∩ ( X 2 < 9 16 )). 1...
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 Spring '07
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 Probability, Probability theory, probability density function, ξ

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