menu
bartleby
search
close search
Hit Return to see all results

5) Given below is a bivariate distribution for the random variables x and y.f(x, y)xy0.250800.530500.34060Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?

Question

5) Given below is a bivariate distribution for the random variables x and y.

f(x, y) x y
0.2 50 80
0.5 30 50
0.3 40 60
  1. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?
  2. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?
check_circleAnswer
Step 1

Obtain the mean of x and mean of y:

The mean of x is, sum(xf(x.y) =E(x)=37 and mean of y is, sum(yf(x.y)=E(y) =59

(xy) f(x y)f(x, y) yxy)f (x y)
f(x, y)
X
y
0.2
800
80
10
16
500
1,280
1,250
0.5
30
50
15
25
450
750
0.3
40
60
12
18
480
1,080
720
120 190
Totals
37
59
1,430
3,610
2,270
help_outline

Image Transcriptionclose

(xy) f(x y)f(x, y) yxy)f (x y) f(x, y) X y 0.2 800 80 10 16 500 1,280 1,250 0.5 30 50 15 25 450 750 0.3 40 60 12 18 480 1,080 720 120 190 Totals 37 59 1,430 3,610 2,270

fullscreen
Step 2

Obtain the variance of x:

The variance of x is,

V(x)-E(x)[E(x)]
-f(xy)-[E(x)
-1,430-(37)
61
help_outline

Image Transcriptionclose

V(x)-E(x)[E(x)] -f(xy)-[E(x) -1,430-(37) 61

fullscreen
Step 3

Obtain the variance of y:

The varian...

V(y)E()E(
-yf(x y)-[E(y)
3,610-(59)
=129
help_outline

Image Transcriptionclose

V(y)E()E( -yf(x y)-[E(y) 3,610-(59) =129

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Bayes' rule can be used to identify and filter spam emails and text messages.In this collection, 747...

A: Given DataP(Spam) = 0.1340P(Not spam) = 1- P(spam) = 1 - 0.1340 = 0.866P(Free) = 0.0475P(Free and sp...

question_answer

Q: What are criterion, convergent, divergent, and diagnostic validity?

A: Criterion-related validity:A test is said to have criterion-related validity, if it helps to predict...

question_answer

Q: What is the critical F value when the sample size for the numerator is twenty one and the sample siz...

A: Here, 

question_answer

Q: help on this problem Problem 5. Suppose X is a random variable with just two possible values a and b...

A: We are given, values of x as a and b.We have to use properties of probability mass function to find ...

question_answer

Q: A random sample of 16 pharmacy customers showed the waiting times below (in minutes).  16 11 21 1...

A: Step-by-step procedure to obtain the mean and standard deviation value using the Excel:In Excel shee...

question_answer

Q: Number of basketball teams (five players) that can be formed from eight players. Note that a basketb...

A: Permutations Rule:Number of ordered arrangement of r objects taken from n objects is denoted as nPr ...

question_answer

Q: 5) Given below is a bivariate distribution for the random variables x and y. Number of Cups per ...

A: Introduction:Hey there! Thank you for the question. However, the data you have posted seems to have ...

question_answer

Q: Suppose the newspaper states that the probability of rain today is 35%. What is the complement of th...

A: Complement of an event:Complement of an event A is the set of all outcomes that are not in the event...

question_answer

Q: 265,000 is borrowed to buy a house. If the simple interest rate on the 30 year loan is 8.25% find th...

A: Given The amount borrowed = $265,000Simple interest = 8.25%Loan tenure = 30 yearsThe total interest ...

Sorry about that. What wasn’t helpful?