Statistical Inference: A Short Course

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.

b.

c.

d.

4. Suppose that for events A and B, we have P(B) = 0.3, , and P(A ∩ B) = 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 ...