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1. Let Y,,denote the nth order statistic of a random sample of size n from a distribution of the continuous type. Find th smallest value of n for which Pr (eo.9 <>Y,,) > 0.75.
2. Let Y1 <>Y2 <>Y3 <>Y4 <>Y5 denote the order statistics of a random sample of size 5 from a distribution of the continuous type. Compute:
(a) Pr ( Y, ,o5 Y5).
(b) Pr ( Y, ,o.25 Y3).
(c) Pr ( Y4 ,o.so Ys).
If f is upper semicontinuous on a compact space S, show that for some t ∈ S, f (t ) = sup f := sup{ f (x ): x ∈ S}. Hint: Let an ∈ R, an ↑ sup f . Consider f -1((-∞, an )), n = 1, 2,... .
the hit-and-miss manufacturing company produces items that have a probabilitypof being defective. these items are
An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are:
wo baseball teams, the Toronto Jaybirds and the Philadelphia Cheesesteaks, are members of a fictitious baseball league. Whenever two teams in this league face each other, they play a series of up to five games. The first team to win three games wi..
What is the probability that a customer does at least one of these two things?
When sampling is done for the proportion of defective items in a large ship- ment, where the population proportion is 0.18 and the sample size is 200, what is the probability that the sample proportion will be at least 0.20?
The U.S. Commission of Crime wishes to estimate the fraction of crimes related to firearms in an area with one of the highest crime rates in the country.
for the white-out football game there are 2000 student tickets total. 1000 of them have already been given out to the
the presence of carbohydrate-deficient transferritin cbt in the blood is a marker for alcohol abuse. a study was
A sample of n = 25 participants and obtains a t statistic of t = 2.21. Which of the following is the correct decision for a two-tailed test?
Assume that 60 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1,000 voters will yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion.
If the average tax payer who makes $140,000 per year owes the government $18,200 with a standard deviation of $1500, and the IRS receives a 1040 tax documents from a customer who earned $140,000 that claims he only owes $12,000, should the IRS sus..
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