(Note, P(Z ≤ 2) = 0.977 , P(Z ≤ 2.054) = 0.98 , P(Z ≤ 2.326) = 0.99 , where Z is standard normally distributed.)
Assume that X and Y are independent and standard normally distributed. Find the conditional mean of X , given that X > Y .
Assume that in a certain population of married couples the height X of the husband and the height Y of the wife have a bivariate normal distribution. The correlation coefficient between the heights of husbands and wives is 0.6 and the mean male height is 173 cm with standard deviation 6 cm, and the mean female height is 161 cm with standard deviation 5 cm.
(1) Given that the height of the husband is 188 cm, the probability that his wife has a height between 160.5 and 176.5 cm is (1)_____ .
(2) The exact distribution of the average height of a couple is (2)_____ .
How would you handle an influential observation in simple linear regression analysis?_____
Define Δp as the daily change for the value of a portfolio in one day. Suppose that one-day volatility of Δp is 2 and Δp from one day to the next day are independent. The estimate of 4-day volatility for Δp is .Suppose that daily changes Δp have first-order correlation with 0.12. The 4-day volatility for Δp will be_____
A simple regression analysis was performed on a random sample, generating he following summary statistics SSx = 250 , SSy = 700 , SSxy = 400 , and n =14 . The F-value for testing a significant relationship for simple regression analysis is _____
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on the five types of analyzers is used. Because tune-up time varies among three types of cars which were used as blocks in the experiment. The data were obtained: SST = 430 , SSTR = 310 , SSBL = 85 . The F-value for testing any significant differences in the mean tune-up time among five analyzers is _____ If the block effect is ignored, the F-test value for testing any significant differences in the mean tune-up time among five analyzers for one-way ANOVA is _____
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