2 6. Show that a gamma distribution with a > 1 has a relative maximum atx = (a- 1)ß. What happens when 0 < a < 1 and a = 1?%3D

Relative maximum =? For a gamma distribution for alpha>1

Answered: 6. Show that a gamma distribution with…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 5SE: What does the y -intercept on the graph of a logistic equation correspond to for a population...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
For a correlation of -.64 between X and Y, each 1 _SD change in Zx corresponds to a predicted change of _____________SD in Zy.
8. Similar to Question 6, consider a portfolio with w invested in asset X and 1- w invested in asset Y for w€ (0,1). The volatilities of asset X and Y are 0.2 and 0.3, respectively. Suppose that the correlation coefficient between the two assets is zero. Express the portfolio variance as a function of w and find the value w* that yields the minimum portfolio variance, i.e. o(w*). Select the best answer that corresponds to the minimum portfolio volatility, op(w*): (a) 16.64% (b) 2% (c) 2.77% (d) 14.14% 9. Stock J has a beta of 1, an expected return of 15%. The equity risk premium is 10%, and the risk-free rate is 2.5%. Calculate Jensen's alpha measure for Stock J. (a) -2.5% (b) 0% (c) 2.5% (d) -7.5% 10. Currently, shares of MJ Corp. trade at $100. The probability of the price increasing by $10 in one day is 30% and the probability of the price decreasing by $10 in one day is 70%. Let R₂ denote log-return on the asset over two days, i.e. R₂ = In (a) 12.96% (b) 13.69% (c) 7.69% (d) 20.96%…
Q. 4 The pdf of the age-of babies, x years, being brought to a clinic is given by /(x) =D 제(2-x); 0
Suppose that there is a correlation of r= 0.41 between the amount of time that each student reports studying for an exam and the student's grade on the exam. This correlation would mean that there is a tendency for people who study more to get better grades.
2. Suppose two researchers independently collect samples of 100 house prices and their floor areas. They each run a regression of house price on floor area (including an intercept) and come up with two estimates of 3₁. Will those estimates be exactly equal? Explain. For now, assume homoskedasticity: Var (e|x) = 0².
Please solve it perfectly
Suppose a positive linear correlation is found between two quantities. Does this mean that one of the quantities increasing causes the other to increase? If not, what does it mean?
A correlation of r = .85 is found between weekly sales of firewood and coughdrops over a 1-year period. Which of the following is true? (a) There is a pretty strong positive linear relationship between sales of firewood and cough drops. (b) Fire must be the cause of coughing. (c) Temperature is a possible lurking variable that is “behind” this relationship. (d) Both (a) and (c) are true. (e) None of the above.
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When the change in a variable 'x' directly causes the change in another variable y' that is an example of: O A. increasing O B. decreasing O C. causation O D. correlation
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6. Show that a gamma distribution with a > 1 has a relative maximum at x = (a- 1)ß. What happens when 0 < a < 1 and a = 1?