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Let X and Y have exponential distributions Exp(3) (i.e, with the parameter 3) We assume that X and Y are independent. Let U=X+2Y and V=-X+Y. Represent (X,Y) as a function of (U,V). Find the joint density f(u,v) for (U,V) (Hint: take into account the region where it is non-zero). Calculate f(1,0) and input it as the answer.
On basis of these data, can college conclude that students in new program performed significantly better than rest of freshman class? Use a one-tailed test with α = .05.
According to state government, the monthly incomes of college graduates have a standard deviation of $650. A county official believes that the standard deviation of monthly incomes is higher in her county.
Dana and Cathy are playing tennis. The probability that Dana wins at least one out of two ames is 0.3. What is the probability that Dana wins at least one out of four?
Would the mean, median, or mode of the prices of recent home sales be the best measure of central tendency and why?
Calculate the population mean and population standard deviation.
Determine a 90% confidence interval for the mean weight of all university male first-year students.
Assuming 250 of each sex, can we conclude that there is a significant difference in the proportions at a 0.05 level of significance?
Determine the distributions given below represent a probability distribution. Justify your answer.
If there are 20 people in the room, 12 men and 8 women, what is the probability of picking two people, without replacement, getting a woman on the first and a man on the second?
What are examples of variables that follow a binomial probability distribution? What are examples of variables that follow a Poisson distribution? When might you use a geometric probability?
Please show all steps to simplifying the rational expression.
Conclude whether the given conditions justify using the methods of this section when testing a claim about a population mean µ.
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