pls answer questions 1 , 2 and 3
1) (25pts) The distribution of loss due to fire damage to a ware- house is given by k P 0 0.8 500 ? 1000 ? 10000 0.08 50000 0.02 100000 0.01 Insurance company charges $2000 premium for a yearly policy in order to break even. a) Determine the missing probabilities of loss in the table. b) Calculate the probability of loss Pk S $1000) c) Calculate the probability of loss Pli> $1000) (both exactly and approximately via Markov's inequality) 2) An insurance policy pays an individual 100 per day for the first 4 days of hospitalization and 50 per day for each day of hospi- talization thereafter. The number of days of hospitalization, X. is a discrete random variable with probability function k=1.2.....9 0 otherwise Calculate the expected payment for hospitalization under this policy. 3) (25pts) An insurance company has 12,000 car policyholders. The expected vearly claim per policyholder is $250 with a standard deviation of $1300. a) What is the probability that the total yearly claim is in between $1 million and $3 million? b) What is the probability that the total yearly claim is less than $2.5 million? c) What is the probability that the total yearly claim exceeds $2.9 million? 10 p(x = 1) = { 1) (25pts) The distribution of loss due to fire damage to a ware- house is given by k P 0 0.8 500 ? 1000 ? 10000 0.08 50000 0.02 100000 0.01 Insurance company charges $2000 premium for a yearly policy in order to break even. a) Determine the missing probabilities of loss in the table. b) Calculate the probability of loss Pk S $1000) c) Calculate the probability of loss Pli> $1000) (both exactly and approximately via Markov's inequality) 2) An insurance policy pays an individual 100 per day for the first 4 days of hospitalization and 50 per day for each day of hospi- talization thereafter. The number of days of hospitalization, X. is a discrete random variable with probability function k=1.2.....9 0 otherwise Calculate the expected payment for hospitalization under this policy. 3) (25pts) An insurance company has 12,000 car policyholders. The expected vearly claim per policyholder is $250 with a standard deviation of $1300. a) What is the probability that the total yearly claim is in between $1 million and $3 million? b) What is the probability that the total yearly claim is less than $2.5 million? c) What is the probability that the total yearly claim exceeds $2.9 million? 10 p(x = 1) = {
