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The random variables X and Y each take values -1 and 1, and p(X=1)=a, P(Y=1)=b. Suppose Z=XY and that X, Y and Z are pairwise independent. What are the values of a and b? are {X,Y,Z} independent?
Using the results, describe the effect of an outlier or extreme value on the confidence interval.
One state lottery has 500 prizes of $1, 75 prizes of $15, 15 prizes of $100, 5 prizes of $450, 2 prizes of $1225, and 1 prize of 2500. Assume that 28,000 lottery tickets are issues and sold for $1. What is the lottery's expected profit per ticket?
The mean amount of a purchase at the Smith Hardware store is $23.50 with standard deviation of $5.00. The amounts purchased follow normal distribution.
You run a two tail t-test. The critical value for this test at the .05 level is a t of 7.82. What value must the obtained t-test statistic be in order to be considered significant at the .05 level?
In the last quarter of 2007 a group of 64 mutual funds had a mean return of 0.9% with a standard deviation of 5.2%. Consider the normal model N(0.009.052) for the returns of these mutual funds.
Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Identify..
Suppose the budget has the support of 52% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
It was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with 6 different professors. What is the probability that all 6 are extroverts?
Using the data, construct a 95% lower confidence interval on mean battery life. Why would the manufacturer be interested in a one-sided confidence interval?
A manager of a supermarket estimated that 87% of customers use coupons in their grocery purchases. How large a sample is required to estimate the true proportion to within 0.01 with 98% confidence?
The random variable x has a normal distribution with mean=30 and standard deviation = 30. Find the probability that x assumes a value more than two standard deviations from its mean more than three standard deviations from the mean.
A slot machine in Reno costs $1 to play. If the jackpot is $1,000 and the expected value is $ - 0.50 find the probability of winning.
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