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Unformatted text preview: 11. (SOA) The distribution of accidents for 84 randomly selected policies is as follows: Number of Accidents Number of Policies 0 32 1 26 2 12 3 7 4 4 5 2 6 1 Total 84 Which of the following models best represents these data?
A) Negative binomial B) Discrete uniform C) Poisson
D) Binomial E) Either Poisson or Binomial 12. (CAS May 06) Total claim counts generated from a portfolio of t,000 policies follows a
Negative Binomial distribution with parameters r = 5 and [3 = 0.2. Calculate the variance in total claim counts if the portfolio increases to 2,000 policies. A) Less than 1.0 B) At least 1.0, but less than 1.5 C) At least 1.5, but less than 2.0 D) At least 2.0, but less than 2.5 B) At least 2.5 13. N has a geometric distribution with a mean of 2. Describe the probability functions, the mean and the variance of the zerotruncated distribution and the zeromodified distribution with M 1
P0:— 6 . l4.(CAS) Vehicles arrive at the Bunand—Run drivethru at a Poisson rate of 20 per hour. On
average, 30% of these vehicles are trucks. Calculate the probability that at least 3 trucks arrive between noon and 1:00 PM.
A) Less than 0.80 B) At least 0.80, but less than 0.85
C) At least 0.85, but less than 0.90 D) At least 0.90, but less than 0.95 E) At least 0.95 15.(CAS) Coins are tossed into a fountain according to a Poisson process with a rate of one every
three minutes. The coin denominations are independently distributed as follows: Coin Denomination Probabiliﬂ
Penny 0.5
Nickel 0.2
Dime 0.2
Quarter 0.1 Calculate the probability that the fourth dime is tossed into the fountain in the first two hours.
A) Less than 0.89 B) At least 0.89, but less than 0.92 C) At least 0.92, but less than 0.95
D) At least 0.95, but less than 0.98 B) At least 0.98 16. (CAS) You are given:  Claims are reported at a Poisson rate of 5 per year.  The probability that a claim will settle for less than $100,000 is 0.9. What is the probability that no claim of $100,000 or more is reported for the next 3 years?
A) 20.59% B) 22.31% C) 59.06% D) 60.65% E) 74.08% 17. (CAS) XYZ Insurance Company introduces a new policy and starts a sales contest for 1000
of its agents. Each makes a sale of the new product at a Poisson rate of 1 per week. Once an
agent has made 4 sales, he gets paid a bonus of $1000. The contest ends after 3 weeks. Assuming 0% interest, what is the cost of the contest?
A) $18,988 B) 357,681 C) $168,031 D) $184,737 E) $352,768 18. (CAS May 2005) For Broward County, Florida, hurricane season is 24 weeks long. It is
assumed that the time between hurricanes is exponentially distributed with a mean of 6 weeks. It
is also assumed that 30% of all hurricanes will hit Broward County. Calculate the probability that in any given hurricane season, Broward County will be hit by more than 1 hurricane.
A) Less than 15% B) At least 15%, but less than 20%
C) At least 20%, but less than 25% D) At least 25%, but less than 30% E) 30% or more i9. (SOA) X is a discrete random variable with a probability function which is a member of the
(a, b, 0) class of distributions. You are given: (5) P(X = 0) = P(X = 1) z .25 (ii) P(X = 2) = .1875. Calculate P(X = 3) . A) 0.120 B) 0.125 C) 0.130 D) 0.135 E) 0.140 20. (80A) For a discrete probability distribution, you are given the recursion relation
ptk)=%p(k1). k:1,2,.... Determine 13(4).
A) 0.07 B) 0.08 C) 0.09 D) 0.10 a) 0.11 21. (SOA) A discrete probability distribution has the following properties:
(i) p), = C(l + %)p;,_1 for k = 1,2, ...(ii) 100 m 0.5 Calculate c.
A) 0.06 B) 0.13 C) 0.29 D) 0.35 E) 0.40 22. (SOA) An actuary has created a compound claims frequency model with the foilowing properties: (i) The primary distribution is the negative binomial with probability generating function
P(z) = [1 « 3(z — 1)]2. (ii) The secondary distribution is the Poisson with probability generating function
13(2) = BAR'1} . (iii) The probability of no claims equals 0.067. Calculate A. A) 0.1 B) 0.4 C) 1.6 D) 2.7 E) 3.1 23. Q has a beta 0., b, 1 distribution (6 = 1, Q is distributed on the interval (0,1) ).
The conditional distribution of Y given Q = g has probability function
It P(Y=le=Q)m(1—+q5jrﬁ You are given that the unconditional mean and variance of Y are
E{Y) = .6 and Varﬂ’) = 1.04. Find the values of a. and b. 24. The distribution of N given P = p is binomial with parameters n and p. If P is I
continuously uniformiy distributed on the interval [0, 1} , what is Var[N} ? 2 2__ 2 2.... 2 2 .
A) 131—2 B) 1112” C) 7115“ D) H.122” E) nil21? 25. An insurer is combining two independent biocks of insurance. The aggregate claims in both
blocks are represented by compound Poisson distributions. With N (1) , N (2) denoting the
number of claims in block 1 and block 2, respectively, and N = N {1) + N {2) , you are given
P[N(1} : 0] = .1108,P[N(2) m 1] 2 .31056 and P[N = 2] a .15394 . What is Pr[N = 1}?
A) .02 B) .04 C) .06 D) .08 E) .10 ...
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 Spring '11
 GABORLUKACS
 Calculus

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