# Objective: To demonstrate that an expected value E(X) is an average, and that there is variation…

Objective: To demonstrate that an expected value E(X) is an
average, and that there is variation around the average. Scenario: A life
insurance company charges \$1,500 for a \$100,000 one-year term life insurance
policy for a 60-year-old white male. If the insured lives, the company gains
\$1,500. If the insured dies, the company loses \$98,500 (the \$100,000 face value
of the policy minus the \$1,500 prepaid premium). The probability of the
insureds death during the year is .012. Instructions: (a) Calculate the
companys expected payout (\$100,000 with probability .012, \$0 with probability
.988).
»

Objective: To demonstrate that an expected value E(X) is an
average, and that there is variation around the average. Scenario: A life
insurance company charges \$1,500 for a \$100,000 one-year term life insurance
policy for a 60-year-old white male. If the insured lives, the company gains
\$1,500. If the insured dies, the company loses \$98,500 (the \$100,000 face value
of the policy minus the \$1,500 prepaid premium). The probability of the
insureds death during the year is .012. Instructions: (a) Calculate the
companys expected payout (\$100,000 with probability .012, \$0 with probability
.988). (b) Calculate the expected net profit by subtracting the expected payout
from \$1,500. (c) To perform a Monte Carlo simulation of net profit for 1,000
insurance policies, enter the Excel formula =IF(RAND()< 0.012,98500,1500))="" into="" cell="" a1="" and="" then="" copy="" the="" formula="" into="" cells="" a1:a1000.="" (d)="" to="" get="" the="" simulated="" net="" profit,="" in="" cell="" c1="" enter="" the="" formula="AVERAGE(A1:A1000)." (e)="" press="" f9="" ten="" times,="" each="" time="" writing="" down="" the="" average="" in="" cell="" c1.="" (f)="" was="" the="" average="" net="" profit="" close="" to="" the="" expected="" net="" payout="" from="" part="" (b)?="" (g)="" to="" count="" the="" number="" of="" times="" the="" company="" had="" to="" pay,="" enter="COUNTIF(A1:A1000," =-98500")"="" in="" cell="" c2.="" (h)="" press="" f9="" ten="" times="" and="" write="" down="" how="" many="" times="" the="" company="" had="" to="" pay.="" bottom="" line="" questions:="" how="" much="" variability="" is="" there="" in="" the="" number="" of="" claims="" paid="" and="" in="" the="" net="" profit="" for="" 1,000="" policies?="" why="" is="" the="" expected="" value="" an="" incomplete="" description="" of="" net="" profit?="" why="" does="" an="" insurance="" company="" need="" to="" issue="" lots="" of="" insurance="" policies="" in="" order="" to="" have="" stable="" profits?="" would="" 1,000="" policies="" be="">

»

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