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## Homework Statement

Ok, I have 2 questions:

1. Nicotine levels in smokers can be modelled by a normal random variable with mean 315 and variance 131

^{2}. What is the probability, if 20 smokers are tested, that at most one has a nicotine level higher than 500?

2. f

_{X,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 = 0.079

^{2}, 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] f

_{X,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?