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1. Choose a number at random from the set of numbers from the set of numbers {1,2,3,4,5}. Now choose a number from the subset {1,...,X). Call this second number Y.
a) Find the joint p.m.f. of X and Y
b) Find the conditional mass function of X given that Y = i. Do it for i = 1,2,3,4,5
c) Are X and Y independent? Why?
Utilizing jacobian method finding the probability density function. Utilizing either the CDF method or Jacobian method illustrate the probability density function of Y is given.
A coin was flipped twenty times and landed heads fifteen times. Based upon this information, answer the following the question:
Critically discuss the Central Limit Theorem? How large should the sample size be if the underlying distribution of the population values are:
Use the F test of ANOVA (assume α = 0.05) to decide whether or not there are any differences in true average lumen outputs between the three brands for this type of light bulb.
Suppose that we generate a random sample from a given dis- tribution. If it is desired that the probability that the sample mean will be within 2 standard deviations of the mean of the distribution is at least .99, how large should the sample size..
What is the probability of selecting a female or an accounting major? Which rule of addition did you apply?
In other words, explain why, all else being equal, as sample size increases the likelihood of finding a statistically significant relationship increases.
Distinguish between a minimization and maximization LP model. Other than minimizing costs and maximizing profits, give a real-world example of where you would want to minimize something or maximize something.
Find the probability of an untrained dog performing as well as Maggie. Is it unusual for an untrained dog to do as well as Maggie?
A prison official wants to estimate the proportion of cases of recidivism. In examining 250 convicts there are 65 cases. with 99% confidence interval what is the range? How do you figure this type of problem?
From historical data, Harry's Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes.
Obtain a test statistic and p-value assuming equal variances. Interpret these results.
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