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Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.2 50 80 0.3 30 50 0.5 40 60 (a) Compute the expected value and the variance for x and y. E(x) = E(y) = Var(x) = Var(y) = (b) Develop a probability distribution for x + y. x + y f(x + y) 130 80 100 (c) Using the result of part (b), compute E(x + y) and Var(x + y). E(x + y) = Var(x + y) = (d) Compute the covariance and correlation for x and y. (Round your answer for correlation to two decimal places.) covariancecorrelation Are x and y positively related, negatively related, or unrelated? The random variables x and y are . (e) Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why? The variance of the sum of x and y is the sum of the variances by two times the covariance, which occurs whenever two random variables are .

Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.2 50 80 0.3 30 50 0.5 40 60 (a) Compute the expected value and the variance for x and y. E(x) = E(y) = Var(x) = Var(y) = (b) Develop a probability distribution for x + y. x + y f(x + y) 130 80 100 (c) Using the result of part (b), compute E(x + y) and Var(x + y). E(x + y) = Var(x + y) = (d) Compute the covariance and correlation for x and y. (Round your answer for correlation to two decimal places.) covariancecorrelation Are x and y positively related, negatively related, or unrelated? The random variables x and y are . (e) Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why? The variance of the sum of x and y is the sum of the variances by two times the covariance, which occurs whenever two random variables are .

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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7. Given below is a bivariate distribution for the random variables x and y.
f(x, y)
 x y
0.2 50 80
0.3 30 50
0.5 40 60
(a)
Compute the expected value and the variance for x and y.
E(x)
=
E(y)
=
Var(x)
=
Var(y)
=
(b)
Develop a probability distribution for 
x + y.
x + y
f(x + y)
130  
80  
100  
(c)
Using the result of part (b), compute 
E(x + y)
 and 
Var(x + y).
E(x + y)
=
Var(x + y)
=
(d)
Compute the covariance and correlation for x and y. (Round your answer for correlation to two decimal places.)
covariancecorrelation
Are x and y positively related, negatively related, or unrelated?
The random variables x and y are      .
(e)
Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?
The variance of the sum of x and y is      the sum of the variances by two times the covariance, which occurs whenever two random variables are      . 
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