- #1
Kate2010
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Homework Statement
Ok, I have 2 questions:
1. Nicotine levels in smokers can be modeled by a normal random variable with mean 315 and variance 1312. What is the probability, if 20 smokers are tested, that at most one has a nicotine level higher than 500?
2. fX,Y (x,y) = xe-x-y 0<x<y<[tex]\infty[/tex]
Find c.
Find the marginal probability density functions.
Homework Equations
The Attempt at a Solution
1. I have worked out that each smoker individually has a 0.079 probability of having a nicotine level higher than 500, but I'm not sure about the at most one section. Would I need to work out 1-P(at least 2 have a nicotine level higher than 500) where P(at least 2 have a nicotine level higher than 500) = P(2 have a nicotine level higher than 500) + P(3 do) + P(4 do) + ... + P(20 do). In this case would it be a geometric sum with a = 0.0792, r = 0.079 and n = 19?
2. It is the limits of integration that I am finding confusing here. I know to find c I need to do the double integral equal to one, but is it [tex]\int[/tex][tex]^{infinity}_{0}[/tex][tex]\int[/tex][tex]^{y}_{0}[/tex] fX,Y (x,y) dx dy (i.e. integrating x between 0 and y and y between 0 and infinity)?
Similarly for the marginal distributions would the limits when integrating with respect to y be 0 and infinity and x be 0 and y?