NullState Insurance insures homes. The insured value, X, of a randomly selected
ID: 3230681 • Letter: N
Question
NullState Insurance insures homes. The insured value, X, of a randomly selected home is assumed to follow a distribution with density function f(x) = 3x^-4 for x > 1, where x is in hundreds of thousands of dollars. a) Find the c.d.f of X. b) Given that a randomly selected home is insured for at least $150,000 what is the probability that it is insured for at least $200,000? c) If 10 homes that NullState insures are picked at random, what is the probability that 5 are insured for at least $150,000?Explanation / Answer
CDF = Integral of PDF where x varies from 1 to infinity
CDF = 3 x^(-4+1) / (-4+1) = -(x^-3) x varies from 1 to infinity
2) Required probabilty = P(Insured for 200000)/ P(Insured for 150000) = (1/2)^3 / (1/1.5)^3 = 0.421875
3) P( Insured for atleast 150000) = 1/(1.5)^3 = 0.29629
Required probability = 10C5 * 0.29629^5 * (1-0.29629)^5 = 10*9*8*7*6/120 *0.29629^5 * (1-0.29629)^5=0.099
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