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Let the random variable Y represent hourly wages and the random variable X represent education. Suppose we have the...
3. Let X be a continuous random variable with E(X)-μ and Var(X)-σ2 < oo. Suppose we...
3. Let X be a continuous random variable with E(X)-μ and Var(X)-σ2 < oo. Suppose we try to estimate μ using these two estimators from a random sample X, , X,: For what a and b are both estimators unbiased and the relative efficiency of μι to is 45n?
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the ...
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the regression equation of ve? (Hint: does this problem affect unbiasedness or c ciency of OLS estimators?) (d) (10 pts bonus) Solve the problem by completely specifying the regression model. 630 pts) Suppose & is the residual of the following regression (a) If we are also running the regression what OLS assumption of time series data we suspect is violated (what time series prob-...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distr...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
3. Suppose we have a random variable X with mean a new random variable Y as...
3. Suppose we have a random variable X with mean a new random variable Y as = 7 and variance a4. We define Y 3 5X Find the standard deviation of Y
Suppose we have the following values for a dependent variable, Y, and three independent variables, X1,...
Suppose we have the following values for a dependent variable, Y, and three independent variables, X1, X2, and X3. The variable X3 is a dummy variable where 1 = male and 2 = female: X1 X2 X3 Y 0 40 1 30 0 50 0 10 2 20 0 40 2 50 1 50 4 90 0 60 4 60 0 70 4 70 1 80 4 40 1 90 6 40 0 70 6 50 1 90 8 80 ...
Suppose we have a sample of observations for the pair of random variable (X, Y) in the following ...
Suppose we have a sample of observations for the pair of random variable (X, Y) in the following 2 x2 Show that the odds ratio can be estimated by ad/bc and derive an estimate of the variance of this estimator
Suppose we have a sample of observations for the pair of random variable (X, Y) in the following 2 x2 Show that the odds ratio can be estimated by ad/bc and derive an estimate of the variance of this estimator
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a...
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
6. Let the random variables X and Y represent the population of two species/organisms that compete...
6. Let the random variables X and Y represent the population of two species/organisms that compete with each other for survival. Suppose that the probability density function p(x, y) of these random variables is proportional to rye-(az+By) (a) What would be an appropriate sample space S for the random variables? Justify your choice of S. (b) Let p(x, y)-Krye-(az-+8v). What should be the proportionality constant K? (c) What is the most probable set of populations (X, Y)? (Hint: The probability...
Exercise 3. We say that a family of random variables (X)teo.) converges in probability to a random variable X (notation...
Exercise 3. We say that a family of random variables (X)teo.) converges in probability to a random variable X (notation: Xt-, X) if for everye> 0, liml+xPfXt-X) > e) = 0. Suppose that (Nt)t20 is a Poisson process of rate X. Show that Nt/t P+ λ. This shows that the rate measures the average frequency or density of arrivals. What about N1 λ?
Exercise 3. We say that a family of random variables (X)teo.) converges in probability to a random...
The guess 0 was marked as incorrect. Suppose we have a random variable X such that...
The guess 0 was marked as incorrect.
Suppose we have a random variable X such that X = 1 with probability 1/2 and X--1 with probability 1 /2. we also have another random variable Y such that Y- X with probability 3/4 and YXwith probability 1/4. What is the covariance between them, Cov(X, Y)?
3. Let X be a continuous random variable with E(X)-μ and Var(X)-σ2 < oo. Suppose we try to estimate μ using these two estimators from a random sample X, , X,: For what a and b are both estimators unbiased and the relative efficiency of μι to is 45n?
(e) Suppose that we reject the null hypothesis, what does that imply about OLS estimatron of the regression equation of ve? (Hint: does this problem affect unbiasedness or c ciency of OLS estimators?) (d) (10 pts bonus) Solve the problem by completely specifying the regression model. 630 pts) Suppose & is the residual of the following regression (a) If we are also running the regression what OLS assumption of time series data we suspect is violated (what time series prob-...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
3. Suppose we have a random variable X with mean a new random variable Y as = 7 and variance a4. We define Y 3 5X Find the standard deviation of Y
Suppose we have a sample of observations for the pair of random variable (X, Y) in the following 2 x2 Show that the odds ratio can be estimated by ad/bc and derive an estimate of the variance of this estimator
Suppose we have a sample of observations for the pair of random variable (X, Y) in the following 2 x2 Show that the odds ratio can be estimated by ad/bc and derive an estimate of the variance of this estimator
2. Suppose we have the simple regression model Y =a+8X:+E, and their OLS coefficient estimators a and b. Answer the following questions. (a) Suppose we multiply X, by 1/2 for all i and do the OLS estimation again using X as the regressor (the independent variable). What will be your new estimators, denoted by ă (intercept) and b (slope)? Compare them with the original OLS estimators a and b, respectively (b) Compare Var[b] and Var[b]. Are they the same or...
6. Let the random variables X and Y represent the population of two species/organisms that compete with each other for survival. Suppose that the probability density function p(x, y) of these random variables is proportional to rye-(az+By) (a) What would be an appropriate sample space S for the random variables? Justify your choice of S. (b) Let p(x, y)-Krye-(az-+8v). What should be the proportionality constant K? (c) What is the most probable set of populations (X, Y)? (Hint: The probability...
Exercise 3. We say that a family of random variables (X)teo.) converges in probability to a random variable X (notation: Xt-, X) if for everye> 0, liml+xPfXt-X) > e) = 0. Suppose that (Nt)t20 is a Poisson process of rate X. Show that Nt/t P+ λ. This shows that the rate measures the average frequency or density of arrivals. What about N1 λ?
Exercise 3. We say that a family of random variables (X)teo.) converges in probability to a random...
The guess 0 was marked as incorrect.
Suppose we have a random variable X such that X = 1 with probability 1/2 and X--1 with probability 1 /2. we also have another random variable Y such that Y- X with probability 3/4 and YXwith probability 1/4. What is the covariance between them, Cov(X, Y)?
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