Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.3 50 80 0.2 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) =
Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.3 50 80 0.2 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) =
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 14E
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Question
Given below is a bivariate distribution for the random variables x and y.
|
f(x, y)
|
x | y |
|---|---|---|
| 0.3 | 50 | 80 |
| 0.2 | 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 ---Select--- positively related negatively related unrelated .
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