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The StatDem party contests elections in two countries, Statland and Statopia, the proportion of support the party has in each country being modelled by the random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form f(x, y) = (k(x + 2y) for 0 < x < 1,0 < y < 1 O elsewhere 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 the StatDem party has the support of more than half the population in each country. Part c) Find the marginal density of the support in Statland evaluated at the point X=1/2. Part d) Find the marginal density of the support in Statopia evaluated at the point Y=1/2.

The StatDem party contests elections in two countries, Statland and Statopia, the proportion of support the party has in each country being modelled by the random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form f(x, y) = (k(x + 2y) for 0 < x < 1,0 < y < 1 O elsewhere 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 the StatDem party has the support of more than half the population in each country. Part c) Find the marginal density of the support in Statland evaluated at the point X=1/2. Part d) Find the marginal density of the support in Statopia evaluated at the point Y=1/2.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The StatDem party contests elections in two countries, Statland and Statopia, the proportion of support the party has in each country being modelled by the random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form f(x, y) = (k(x + 2y) for 0 < x < 1,0 < y < 1 O elsewhere 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 the StatDem party has the support of more than half the population in each country. Part c) Find the marginal density of the support in Statland evaluated at the point X=1/2. Part d) Find the marginal density of the support in Statopia evaluated at the point Y=1/2.
Transcribed Image Text:The StatDem party contests elections in two countries, Statland and Statopia, the proportion of support the party has in each country being modelled by the random variables X and Y respectively. It is thought that the joint density function for the two variables is of the form f(x, y) = (k(x + 2y) for 0 < x < 1,0 < y < 1 O elsewhere 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 the StatDem party has the support of more than half the population in each country. Part c) Find the marginal density of the support in Statland evaluated at the point X=1/2. Part d) Find the marginal density of the support in Statopia evaluated at the point Y=1/2.
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