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posted by  questionman on 11/7/2009 12:27:02 PM  |  status: Closed  |  Earned Karma: 25

Probability Density Function

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Statistics and Probability N/A N/A N/A 11/8/2009 at 1:00:00 PM
Question Details:
Let Y be the continuous random variable with density:



a) Find c so that f(y) is a density function.

b) Find P(Y>2)

c) Find the expected value.

d) What is E(2X+3)?
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posted by Jonpp on 11/7/2009 12:46:22 PM  |  status: Live
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Response Details:
(a) Since it is exponential distribution with β=1/2 (or λ=2), c=1/β=λ=2.

(b) F(y)=1-exp(-2y), y>0
P(Y>2)=1-F(2)= 1-1+exp(-2*2)=exp(-4)=0.0183

(c)mean=1/λ=1/2

(d)E(2X+3)=2E(X)+3=2(1/2)+3=4
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