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Question: (a) Give an example of r.v.s X and Y such that FX(x) ≤ FY (x) for all x, where the inequality is strict for some x. Here FX is the CDF of X and FY is the CDF of Y. For the example you gave, sketch the CDFs of both X and Y on the same axes. Then sketch their PMFs on a second set of axes.
(b) In Part (a), you found an example of two different CDFs where the first is less than or equal to the second everywhere. Is it possible to find two different PMFs where the first is less than or equal to the second everywhere? In other words, find discrete r.v.s X and Y such that P(X = x) ≤ P(Y = x) for all x, where the inequality is strict for some x, or show that it is impossible to find such r.v.s.
Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.
A statistics instructor wonders whether there is a significant difference in her student's GPA for each of her three sections. Determine the upper-tail critical value from the F-distribution
a. Fit a simple linear regression model by ordinary least squares and obtain the residuals. Also obtain s{b0} and s{b1}. b. Plot the residuals against time and explain whether you find any evidence of positive autocorrelation.
What is the variance of W in this case? Is it less than, greater than or equal to the variance in (a)? Explain why. For what values of c, if any, will the variance be equal to 0? Explain.
A company is creating 5 new divisions and 8 managers are eligible to be appointed head of a division. With 8 managers trying for 5 jobs, how could the five new heads be arranged?
Explain why this is an observational study, not a randomized experiment.- What were the explanatory and response variables of interest to the researchers?
Suppose we have a population of scores with a mean (μ) of 200 and a standard deviation (σ) of 10. Assume that the distribution is normal. What score would cut off the top 5 percent of scores?
one environmental group did a study of recycling habits in a california community. it found that 72 of the aluminum
a brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of
What was the correlation between health and education and how much variability in health could be accounted for by activity?
the housing market has recovered slowly from the eonomic crisis of 2008. recently in one large community relators
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 925 hours. A random sample of 39 light bulbs has a mean life of 905 hours with a standard deviation o 55 hours.
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