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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- 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."