Determine the correlation coefficient of the random variables X and Y if var(X) = 4, var(Y ) = 2, and var(X + 2Y ) = 15.

Hana Buck 2022-09-23 Answered
Determine the correlation coefficient of the random variables X and Y if var(X) = 4, var(Y ) = 2, and var(X + 2Y ) = 15.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Nancy Phillips
Answered 2022-09-24 Author has 12 answers
The correlation coefficient of X and Y is
ρ X , Y = C o v ( X , Y ) σ X σ Y .
By the properties of variance
V a r ( X + 2 Y ) = V a r ( X ) + 2 2 V a r ( Y ) + 2 1 2 C o v ( X , Y )
= σ X 2 + 4 σ Y 2 + 4 ρ σ X σ Y ,
and from the fact that
Var(X+2Y)=15
it follows that
σ X 2 + 4 σ Y 2 + 4 ρ σ X σ Y = 15
4 + 4 2 + 4 ρ 4 2 = 15
which implies that
ρ = 0.27
Result:
ρ = 0.27
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a 99% confidence interval for the proportion of adult residents who are parents in a given county.
Express your answer in the form of three inequalities. Provide your responses in decimal fractions up to three places <p< Express the same answer using a point estimate and a margin of error. Provide your responses as decimals, to three places.
p=±

asked 2021-03-18

A population of values has a normal distribution with μ=133.5 and σ=5.2. You intend to draw a random sample of size n=230.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
P(133.6<X<134.1)=?
Write your answers as numbers accurate to 4 decimal places.

asked 2021-01-02

The amount of time, in minutes, for an airplane to obtain clearance for take off at a certain airport is a random variable Y=3X-2, where X has the density function
f(x)={14ex4,x>00,else where 
Find the mean and variance of the random variable Y?

asked 2022-09-08
Classify each of the following random variables as discrete or continuous. W = the exact amount of sleep that a randomly selected student from your school got last night.
asked 2022-01-16
What are the mean and standard deviation of a binomial probability distribution with n=169 and p=113?
asked 2022-01-28
How do I calculate the variance and standard deviation of 102, 104, 106, 108, 110?
asked 2021-11-06
If X is a normal random variable with parameters
μ=10
and
σ2=36
, compute P[X>5]

New questions