Question

In: Math

Let X be a random variable representing the number of years of education an individual has,...

Let X be a random variable representing the number of years of education an individual has, and let Y be a random variable representing an individual’s annual income. Suppose that the latest research in economics has concluded that:

Y = 6X +U

(1)

is the correct model for the relationship between X and Y , where U is another random variable that is independent of X. Suppose Var(X) = 2 and Var(Y ) = 172.

a. Find Var(U).

b. Find Cov(X, Y ) and corr(X, Y ).

c. The variance in Y (income) comes from variance in X (education) and U (other factors unobserved to us). What fraction of the variance in income is explained by variance in education?

d. How does the fraction you found in (c) compare to corr(Y, X)?

Solutions

Expert Solution


Related Solutions

Let X be the random variable representing the number of calls received in an hour by...
Let X be the random variable representing the number of calls received in an hour by a 911 emergency service. A probability distribution of X is given below. Value of X 0 1 2 3 4 Probability P(x) 0.32 ____ ____ 0.16 0.08 (a) Suppose the probability that X = 1 and the probability that X = 2 are the same. What are these probabilities? Incorrect: Your answer is incorrect. (b) What is the probability that at least one call...
At a used dealership, let X be an independent variable representing the age in years of...
At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent variable representing the selling price of used motorcycle. The data is now given to you. X = {5, 10, 12, 14, 15} Y = {500, 400, 300, 200, 100} 1) What is the value for S^2? 2) What is the value for s? 3) Construct a 95% confidence interval for B1. what is the upper bound and...
Two dice are rolled. Let X be the random variable representing the result of the first...
Two dice are rolled. Let X be the random variable representing the result of the first die, and Y be the random variable representing the largest value rolled on either die. Describe the joint probability density function for X and Y .
Let X be a random variable representing a quantitative daily market dynamic (such as new information...
Let X be a random variable representing a quantitative daily market dynamic (such as new information about the economy). Suppose that today’s stock price S0 for a certain company is $150 and that tomorrow’s price S1 can be modeled by the equation S1 = S0 · eX. Assume that X is normally distributed with a mean of 0 and a variance of 0.5. (a) Find the probability that X is less than or equal to 0.1 (b) Suppose the daily...
Let x be a random variable representing percentage change in neighborhood population in the past few...
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 31 1 11 17 7 6 y 177 39 132 127 69 53 In this setting we have Σx = 73, Σy = 597, Σx2 = 1457, Σy2 = 73,973, and Σxy = 9938. What percentage of...
QUESTION 1 Let x be a random variable representing the monthly cost of joining a health...
QUESTION 1 Let x be a random variable representing the monthly cost of joining a health club. We may assume that x has a normal distribution and that the population standard deviation is $5.20. A fitness magazine advertises that the mean monthly cost of joining a health club is $35. You work for a consumer advocacy group and are asked to test this claim. You find that a random sample of 40 health club monthly costs has a mean of...
Let x be a random variable representing percentage change in neighborhood population in the past few...
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. PLEASE HELP WITH QUESTIONS (F) - (I) x 28 1 11 17 7 6 y 170 38 132 127 69 53 In this setting we have Σx = 70, Σy = 589, Σx2 = 1280, Σy2 = 71,467,...
Let x be a random variable representing percentage change in neighborhood population in the past few...
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 27 3 11 17 7 6 y 167 40 132 127 69 53 In this setting we have Σx = 71, Σy = 588, Σx2 = 1233, Σy2 = 70,612, and Σxy = 9041. (e) For a...
Let x be a random variable representing percentage change in neighborhood population in the past few...
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 26 2 11 17 7 6 y 179 34 132 127 69 53 In this setting we have Σx = 69, Σy = 594, Σx2 = 1175, Σy2 = 74,320, and Σxy = 9134. (a) Find x,...
Let X be a random variable representing a quantitative daily market dynamic (such as new information...
Let X be a random variable representing a quantitative daily market dynamic (such as new information about the economy). Suppose that today’s stock price S0 for a certain company is $120 and that tomorrow’s price S1 can be modeled by the equation S1 = S0 · e X. Assume that X is normally distributed with a mean of 0 and a variance of 0.25. (a) Find the probability that X is less than or equal to 0.1. (b) Suppose the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT