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 .
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 .
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 .
Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
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