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Statistical Inference: A Short Course by Michael J. Panik

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Exercises

1. Which of the following numbers could not be the probability of an event?
0.0, 1.2, 0.8, 0.0001, −0.7, −1.4, 1.0
2. Describe the following situations:
a. Events A and B are disjoint.
b. Events C and D are complements. (Are C and D also disjoint?)
3. Suppose for events A and B, we have P(A) = 0.25 and P(B) = 0.45. Find the following:
a. img
b. img
c. img
d. img
4. Suppose that for events A and B, we have P(B) = 0.3, img, and P(AB) = 0.12. Find P(A).
5. For a random experiment, let the sample space appear as S = {1, 2, 3, 4, 5, 6, 7, 8} and suppose the simple events in S are equiprobable. Find the following:
a. The probability of event A = {1, 2, 3}
b. The probability of event B = {2, 3, 6, 7}
c. The probability of event C = {an even integer}
d. The probability of event D = {an odd integer}
e. The probability that A and B occurs
f. The probability that A or B occurs
g. P(S)
h. The probability that C and D occurs
i. The probability that A does not occur
j. The probability ...

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