Find a) the mean function for {x,}. b) the variance function for {x,}. c) the covariance for {x,}.
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- If X~Gamma(4,6) the the variance of X is 4 24 144 LOShow that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter 0.A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
- Suppose X~ Uniform [10, 50], find: P70 Variance (X)Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? Explain
- Prove variance property: var(aX +b) = a²var(X) where a and b are constants.I For Poisson's distribution prove that Variance =A dietician is researching two new weight gain supplements that have just hit the market: Ripped and Gainz. She wants to determine if there is any difference between the two supplements in the mean amount of weight gained (in kg) by the people who take them. The dietician tracks the total weight gain (in kg) over a year of a random sample of 14 people taking Ripped and a random sample of 12 people taking Gainz. (These samples are chosen independently.) These data are shown in the table. Total weight gains (in kg) Ripped Gainz 14.1, 10.9, 12.1, 5.2, 12.0, 17.1, 9.0, 14.8, 11.2, 6.8, 12.4, 8.5, 12.1, 10.5 Send data to calc... v 7.6, 9.5, 8.6, 10.8, 7.9, 10.0, 8.4, 6.2, 8.6, 10.2, 8.9, 8.2 Send data to Excel Assume that the two populations of weight gains are approximately normally distributed. Can the dietician conclude, at the 0.05 level of significance, that there is a difference between the population mean of the weights gained by people taking Ripped and the population mean of the…
