Let X ∼ N (µ1, 1) and Y ∼ N (µ2, 1) (same variances, different means) be independent r.v.s. Find the PDF of X + Y .(Hint: You’ll need to complete the square in the exponent.)
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A: see the attachment
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Let X ∼ N (µ1, 1) and Y ∼ N (µ2, 1) (same variances, different means) be independent r.v.s. Find the
(Hint: You’ll need to complete the square in the exponent.)
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- For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)If our data were a perfect fit to our regression model, such that y; = ŷ;, we would expect | to be in the CI on p.Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
- There are 3000 stocks in the long-short stock market, which will be traded for 250 days in the next year. Set X and Y to be the daily holding amount of each stock And the return of the next day, and X and Y are respectively sampled from the normal distribution of N (0.100000NO, 2E-2). Use enough data to estimate Calculate the R2 of X and Y linear regression to be 001. Assume that positions among stocks are not correlated, and returns between stocks are not correlated. Define a day’s PNL as the day’s receipt beneficial PNL= 3000∑xy Find the expectation of PN and the sharpe rate of PNL every dayThe built-in data set, rock, is a data frame recording the measurements of rock sample from a petroleum reservoir. We are interested in the area column of rock. Using R we can convert this column into the vector x by the assignment x30 we can create a confidence interval for μ using a normal critical value. If we want the confidence interval to be at the 94% level and we use a normal critical value, then what critical value should we use? i) Calculate a 94% confidence interval(using a normal critical value) for μ.Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
- Please solve this question.Thanks for your help :)Consider a simple regression Y = B1 + B2 X + u. Suppose we found out that the variance of error term is changing with larger values of X (heteroscedasticity). Show how you overcome the problem of heteroscedasticity by using White’s heteroscedasticity consistent variances (only for variance of the slope estimate). Show and explain.2
- Below are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to ExcelThe variance of temperatures (Fahrenheit) in Las Vegas, Nev. is 327.84. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]Suppose you have a survey where one of the variables is "Sex", and all of the 300 people surveyed answered one of the following: 1) Male or 2) Female. Suppose further that you create 2 dummy variables: D1 = 1 if male, zero otherwise D2 = 1 if female, zero otherwise What would happen if you include both dummy variables in your regression in Excel? O Excel will not be able to run a regression with both variables in the regression. Nothing. This is the correct way to do it. O Your regression will exhibit serial correlation. O Your regression will exhibit some multicollinearity, but can be remedied with "robust standard errors."
