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A 4-faced die weighted so that P(p)/P(k) = 9/2 for all prime p and non-prime natural numbers k satisfying 1 < p, k < 4 is rolled twice (indep Write X for the maximum and Y for the sum of the numbers that appear. (1) (a) Find the joint distribution h(x,y) = P(X = x,Y = y),

A 4-faced die weighted so that P(p)/P(k) = 9/2 for all prime p and non-prime natural numbers k satisfying 1 < p, k < 4 is rolled twice (indep Write X for the maximum and Y for the sum of the numbers that appear. (1) (a) Find the joint distribution h(x,y) = P(X = x,Y = y),

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A 4-faced die weighted so that P(p)/P(k) = 9/2 for all prime p and non-prime natural numbers k satisfying 1 < p, k < 4 is rolled twice (independently). Write X for the maximum and Y for the sum of the numbers that appear. (i) (a) Find the joint distribution h(x, y) = P(X = x,Y = y), where 1 < z < 4 and 2 < y < 8 are natural numbers, of the random variables X, Y, and then enter the values h(k, l), along with the values of the marginal distribution associated with the variable X, in the four input fields below. Observe that the input fields are labelled by the values 1, 2, 3, 4 of the random variable X, and so you have to enter the values h(k, 2), h(k, 3), h(k, 4), h(k, 5), h(k, 6), h(k, 7), h(k, 8), h(k, l) separated by commas, similar to 3 0,0, 2/16, 2/16, 1/16,0,0, 5/16 in the input field labelled a number k; thus in each case you have to enter nine rational numbers (the values h(k, *) and their total). Please don't ignore the zero values of the function h! To facilitate the subsequent calculations, all rational numbers can be entered 'as they are', that is, not necessarily in reduced form. 1 4 (b) Next, enter the totals of all columns (ToC) of the table formed by the numbers you've entered in the input fields above: Тос (ii) Use (i) to find the numerical characteristics of the random variable X (here and everywhere below, all rational numbers are to entered in reduced form; please round the value of the standard deviation of X to a 5-digit floating-point number): Е(X) — E(X²) = Var(X) = ox = (i) Use (i) to find the numerical characteristics of the random variable Y (again, please round the value of the standard deviation of Y to a 5-digit floating-point number): E(Y) = E(Y²) = Var(Y) = oy = (iv) Use (i) to find the expected value E(XY) of the product XY of the random variables X and Y: E(XY) = (v) Use (ii,i,iv) to find the covariance Cov(X, Y) of X and Y: Cov(X, Y) = (vi) Use (ii,ii,iv) to find the correlation p(X, Y) of X and Y (this time, please round your answer to a 5- digit floating-point number): P(X,Y) =
Transcribed Image Text:A 4-faced die weighted so that P(p)/P(k) = 9/2 for all prime p and non-prime natural numbers k satisfying 1 < p, k < 4 is rolled twice (independently). Write X for the maximum and Y for the sum of the numbers that appear. (i) (a) Find the joint distribution h(x, y) = P(X = x,Y = y), where 1 < z < 4 and 2 < y < 8 are natural numbers, of the random variables X, Y, and then enter the values h(k, l), along with the values of the marginal distribution associated with the variable X, in the four input fields below. Observe that the input fields are labelled by the values 1, 2, 3, 4 of the random variable X, and so you have to enter the values h(k, 2), h(k, 3), h(k, 4), h(k, 5), h(k, 6), h(k, 7), h(k, 8), h(k, l) separated by commas, similar to 3 0,0, 2/16, 2/16, 1/16,0,0, 5/16 in the input field labelled a number k; thus in each case you have to enter nine rational numbers (the values h(k, *) and their total). Please don't ignore the zero values of the function h! To facilitate the subsequent calculations, all rational numbers can be entered 'as they are', that is, not necessarily in reduced form. 1 4 (b) Next, enter the totals of all columns (ToC) of the table formed by the numbers you've entered in the input fields above: Тос (ii) Use (i) to find the numerical characteristics of the random variable X (here and everywhere below, all rational numbers are to entered in reduced form; please round the value of the standard deviation of X to a 5-digit floating-point number): Е(X) — E(X²) = Var(X) = ox = (i) Use (i) to find the numerical characteristics of the random variable Y (again, please round the value of the standard deviation of Y to a 5-digit floating-point number): E(Y) = E(Y²) = Var(Y) = oy = (iv) Use (i) to find the expected value E(XY) of the product XY of the random variables X and Y: E(XY) = (v) Use (ii,i,iv) to find the covariance Cov(X, Y) of X and Y: Cov(X, Y) = (vi) Use (ii,ii,iv) to find the correlation p(X, Y) of X and Y (this time, please round your answer to a 5- digit floating-point number): P(X,Y) =
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