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Suppose that X is a discrete random variable with: P(X=0) = (2/3)theta P(X=1) = (1/3)theta P(X=2) = (2/3)(1-theta) P(X=3) = (1/3)(1-theta) where theta: [0,1] is a parameter. The following 10 independent observations were taken from such a distribution: (3,0,2,1,3,2,1,0,2,1)
a. Find the moment of methods estimate of theta
b. Find an approximate standard error for your estimate
c. What is the maximum likelihood estimate of theta?
d. What is an approximate standard error of the maximum likelihood estimate?
Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes were selected at random. What is the probability all three homes selected have a security system?
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Suppose that the null hypothesis is rejected and that an alternate hypothesis is accepted. Discuss the conclusion as a type I error, a type II error, or a correct decision-if in fact the defendant is innocent.
A university wants to determine the proportion of students who use a cash card to pay at the university food service. Out of 100 students surveyed, 65 students use a cash card. Estimate the value of the population proportion.
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1. do this exercise by hand. a famous brand-name manufacturer wants to know whether people prefer nibbles or wribbles.
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