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)

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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Question

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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