209. Let X be a random variable with density function

 Calculate P [X≤0.5|X≤1.0].
(A) 0.433
(B) 0.547
(C) 0.632
(D) 0.731
(E) 0.865

210. Events E and F are independent. P[E] = 0.84 and P[F] = 0.65. Calculate the probability that exactly one of the two events occurs. (A) 0.056 (B) 0.398 (C) 0.546 (D) 0.650 (E) 0.944

211. A flood insurance company determines that N, the number of claims received in a month, is a random variable with P[N=n]= , for n=0,1,2,.... The numbers of claims received in different months are mutually independent. Calculate the probability that more than three claims will be received during a consecutive two-month period, given that fewer than two claims were received in the first of the two months. (A) 0.0062 (B) 0.0123 (C) 0.0139 (D) 0.0165 (E) 0.0185

212. Patients in a study are tested for sleep apnea, one at a time, until a patient is found to have this disease. Each patient independently has the same probability of having sleep apnea. Let r represent the probability that at least four patients are tested. Determine the probability that at least twelve patients are tested given that at least four patients are tested. (A)(B)r3 (C)(D)r2 (E)

213. A factory tests 100 light bulbs for defects. The probability that a bulb is defective is 0.02. The occurrences of defects among the light bulbs are mutually independent events. Calculate the probability that exactly two are defective given that the number of defective bulbs is two or fewer. (A) 0.133 (B) 0.271 (C) 0.273 (D) 0.404 (E) 0.677

214. A certain town experiences an average of 5 tornadoes in any four year period. The number of years from now until the town experiences its next tornado as well as the number of years between tornados have identical exponential distributions and all such times are mutually independent Calculate the median number of years from now until the town experiences its next tornado. (A) 0.55 (B) 0.73 (C) 0.80 (D) 0.87 (E) 1.25

215. Losses under an insurance policy are exponentially distributed with mean 4. The deductible is 1 for each loss. Calculate the median amount that the insurer pays a policyholder for a loss under the policy. (A) 1.77 (B) 2.08 (C) 2.12 (D) 2.77 (E) 3.12

216. A company has purchased a policy that will compensate for the loss of revenue due to severe weather events. The policy pays 1000 for each severe weather event in a year after the first two such events in that year. The number of severe weather events per year has a Poisson distribution with mean 1. Calculate the expected amount paid to this company in one year. (A) 80 (B) 104 (C) 368 (D) 512 (E) 632

217. A company provides each of its employees with a death benefit of 100. The company purchases insurance that pays the cost of total death benefits in excess of 400 per year. The number of employees who will die during the year is a Poisson random variable with mean 2. Calculate the expected annual cost to the company of providing the death benefits, excluding the cost of the insurance. (A) 171 (B) 189 (C) 192 (D) 200 (E) 208

218. The number of burglaries occurring on Burlington Street during a one-year period is Poisson distributed with mean 1. Calculate the expected number of burglaries on Burlington Street in a one-year period, given that there are at least two burglaries. (A) 0.63 (B) 2.39 (C) 2.54 (D) 3.00 (E) 3.78

219. For a certain health insurance policy, losses are uniformly distributed on the interval [0, 450]. The policy has a deductible of d and the expected value of the unreimbursed portion of a loss is 56. Calculate d. (A) 60 (B) 87 (C) 112 (D) 169 (E) 224

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