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Suppose that Z is a random variable with a N(0, 1) distribution. Define a stochastic process via X(t) = (?t)Z, and note that for each t > 0, X(t) has a N(0, t) distribution. Is this Brownian motion?
SOLUTION: No. Increments are not independent; they all contain the same rv Z. For example X(2) ? X(1) = Z, and X(4) ? X(3) = Z, they are the same hence not independent.
a family plans to have 3 children. for each birth assume that the probability of a boy is the same as the probability
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Construct a 95% confidence interval estimate of their mean weight.
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The starting salaries of individuals with an MBA degree are normally distributed with mean of $40,000 and standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000?
A company is filling bags of rock salt to a level of 50 pounds. It believes that all bags are filled correctly, but would like to use a hypothesis test with an alpha of 0.05 to check this belief. The company will be using samples of 100 bags from eac..
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D. The Sunbeam Corporation makes a wide variety of appliances for the home. One product is a digital blood pressure gauge. For obvious reasons, the blood pressure readings made by the monitor need to be accurate.
Graph the p.d.f and show that the probability of the part failing in the first 200 weeks is 1/8
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