1.Two dice are tossed 432 times. How many times would youexpect to get a sum of 5?
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2.Sam is applying for a single year life insurance policyworth $35,750.00. If the actuarial tables determine that she willsurvive the next year with probability 0.996, what is her expectedvalue for the life insurance policy if the premium is $433.00?
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3.A raffle is being held at a benefit concert. The prizes areawarded as follows: 1 grand prize of
$6,200.00, 3 prizes of $1,000.00, 4 prize of $92.00, and 12prizes of $25.00.
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4.Find the expected value for the random variable:
X 1 3 4 6
P(X) 0.21 0.12 0.23 0.44
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5.Suppose that from a standard deck, you draw three cardswithout replacement. What is the expected number of aces that youwill draw?
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6.Consider 3 trials, each having the same probability ofsuccess. Let
X
X
denote the total number of successes in these trials. IfE[X]=0.6, find each of the following.
(a) The largest possible value of P{X=3}:
P{X=3}≤
(b) The smallest possible value of P{X=3}:
P{X=3}≥
In this case, give possible values for the remainingprobabilities:
P{X=0}=
P{X=1}=
P{X=2}=
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7.It is reasonable to model the number of winter storms in aseason as with a Poisson random variable. Suppose that in a goodyear the average number of storms is 5, and that in a bad year theaverage is 8. If the probability that next year will be a good yearis 0.3 and the probability that it will be bad is 0.7, find theexpected value and variance in the number of storms that willoccur.
expected value =
variance =
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8.In a popular tale of wizards and witches, a group of themfinds themselves in a room with doors which change position, makingit impossible to determine which door is which when the room isentered or reentered. Suppose that there are 4 doors in the room.One door leads out of the building after 3 hours of travel. Thesecond and third doors return to the room after 5 and 5.5 hours oftravel, respectively. The fourth door leads to a dead end, the endof which is a 2.5 hour trip from the door.
If the probabilities with which the group selects the fourdoors are 0.2, 0.1, 0.1, and 0.6, respectively, what is theexpected number of hours before the group exits the building?
E[Number of hours]=
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9.For a group of 100 people, assuming that each person isequally likely to have a birthday on each of 365 days in the year,compute
(a) The expected number of days of the year that are birthdaysof exactly 4 people:
E[days with 4 birthdays]=
(b) The expected number of distinct birthdays:
E[distinct birthdays]=
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10.Consider 35 independent flips of a coin having probability0.5 of landing on heads. We say that a changeover occurs when anoutcome is different from the one preceding it. Find the expectednumber of changeovers.
E[changeovers]=
