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Use computer simulation to find the probability that the triangle OAB has an angle larger than 90° when A and B are randomly chosen points within the unit circle having the point O as center. What is this probability if the unit sphere is taken instead of the unit circle? Also, simulate the probabilities of getting a triangle with an obtuse angle from three random points in the unit circle and from three random points in the unit sphere.
Draw suitable distribution curve indicating position of the TS and CV.
2. The p-value for a hypothesis test has been reported as 0.03. If the test result is interpreted using the α = 0.05 level of significance as a criterion, will H0 be rejected? Explain.
Suppose X and Y are independent random variables with X ~ Pois(?1) and Y ~ Pois(?2). Is X + Y a Poisson random variable?
Mean 52 and standard deviation 7; N(52, 7). According to the 68-95-99.7 rule, what percentage of jazz CDs play between 38 and 59 minutes?
a machine dispenses water into a glass. assuming that the amount of water dispensed follows a continuous uniform
Create an equation for which the appropriate test of the statistical hypothesis would require the use of a z-score. (For the population mean for the variable of interest, you may invent a hypothetical population mean for the sake of this equation...
Calculate the t test statistic. Can you reject ρ = 0? (e) Use Excel's function =TDIST(t,deg_freedom,tails) to calculate the two-tail p-value.
a decision maker is interested in estimating a population proportion. a sample of size n 150 yields 115 successes.
For each of the following three populations, indicate what the sampling distribution for samples of 25 would consist of: Travel expense vouchers for a university in an academic year.
To illustrate that the mean of a random sample is an unbiased estimate ofthe population mean, consider five slips of paper numbered 3, 6, 9, 15, and 27
Consider the domain of dealing 5-card poker hands from a standard deck of 52 cards, under the assumption that the dealer is fair.
Constructing a p chart for mishandled baggage. The Department of Transportation reports that 3.22 of every 1000 passengers on domestic flights.
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