The governments in two countries, Statland and Statopia, are proposing to change their national currencies to the Statto. The proportion of support for such a change within the population in Statland and Statopia are modelled by random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form S k(2x + 3y) for 0 < x < 1,0 < y < 1 O elsewhere f(x, y) = for some constant k. Give answers to the following to 2 decimal places. Part a) Find the value of k. Part b) Find the probability that changing to the Statto has the support of more than half the population in each country. Part c) Find the marginal density of the support for the Statto in Statland evaluated at the point X=1/2.
The governments in two countries, Statland and Statopia, are proposing to change their national currencies to the Statto. The proportion of support for such a change within the population in Statland and Statopia are modelled by random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form S k(2x + 3y) for 0 < x < 1,0 < y < 1 O elsewhere f(x, y) = for some constant k. Give answers to the following to 2 decimal places. Part a) Find the value of k. Part b) Find the probability that changing to the Statto has the support of more than half the population in each country. Part c) Find the marginal density of the support for the Statto in Statland evaluated at the point X=1/2.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:The governments in two countries, Statland and Statopia, are proposing to change their national currencies to the Statto. The proportion of support
for such a change within the population in Statland and Statopia are modelled by random variables X and Y respectively. It is thought that the joint
density function for the two variables is of the form
S k(2x + 3y) for 0 < x < 1,0 < y < 1
0 elsewhere
f(x, y) =
for some constant k. Give answers to the following to 2 decimal places.
Part a)
Find the value of k.
Part b)
Find the probability that changing to the Statto has the support of more than half the population in each country.
Part c)
Find the marginal density of the support for the Statto in Statland evaluated at the point X=1/2.
Part d)
Find the marginal density of the support for the Statto in Statopia evaluated at the point Y=1/2.
Part e)
Find the conditional density of the support for the Statto in Statland given the support of a third of the population in Statopia. Evaluate this density at
the point X=1/2.
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