( 10 points ) ( 459 only ) The value of an asset S at time I is modeled as a random variable I with probability density* $ = 0 $ = = f = 0 for * _...

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2. ( 10 points ) ( 459 only ) The value of an asset S at time I is modeled as a randomvariable I with probability density*$ = 0$ = =f = 0for * _ O, ford = = = 5, for I _ 5.Call and put options with strike Is based on this asset have payoff's1 9 ( ` ) =_ ] I - K, I Z K0 .\I S K "\1 P ( I ) =\ K - * , * < Ka ) Calculate ES IT!] , the expected value of S (T ) .b ) Find the expected payoff E [ AC ( S ( T ; ]] for KT = 3.C ) Show AP ( I ) - 1" ( 1) = K - I , and use this identity with the results from a ) and b ) tofind FLAP ( S IT Ill for K< = 3.