# Expected Monetary Value Stats Assignment Homework Help

Expected Monetary Value

When the numbers being averaged are in monetary units, say, United States dollars, expected value is often referred to as expected monetary value and symbolized by EMV. It is computed in the same way as other expected values.
EXAMPLE A fire insurance company assigns a probability of 0.001 that a particular type of building will be completely destroyed by fire during a year, in which case the company will have to pay the insured 100 percent of the value of the building. Similarly, the probabilities of 50 percent and 10 percent damage to the building are, respectively, 0.004 and 0.005. The company classifies all damage as being in one of these three categories. As a first step in determining the amount to be paid for insurance on the building, the company finds the expected monetary value of losses that will 6000 if the building is damaged by fire. The amount to be paid by the buyer of the insurance is called the premium. The premium is larger than the expected loss because the insurance company has to cover expenses and make a profit.The part of the premium which is for expenses and profit is called the loading. (a) If the value of the building is \$80,000, compute the expected value of the loss E(L). (b) If the loading is 30 percent of the premium, compute the premium.
SOLUTION
a. Table 6.2 summarizes the given data and shows the computation of the expected value of the loss E(L) = \$280.
TABLE 6.2
CALCULATING THE EXPECTED LOSS

The difference between the premium, \$400, and the expected loss, \$280, is \$120. Note that \$120is 30 percent of the \$400 premium, as required.
EXERCISE Following the last example, (a) find the expected loss for a  building valued at \$20,000; (b) find the premium if the loading is 25 percent of the premium.
Expected value calculations may involve both gain and loss (negative gain) events.

EXAMPLE In the carnival game of queens, the operator shuffles six cards and places them face down on a table. Two of the cards are kings, two are queens, and two are jacks. The player, called the “mark” in carnival language, selects two cards. The operator bets the mark \$5 even money that at least one of the selected cards is a queen. What is the mark’s expected value in playing this game?

SOLUTION The bet means the mark wins \$5 or loses \$5. The outcomes for the mark are expressed as \$5 and – \$5. The mark wins if neither of the two selected cards is a queen. Because there are 4 nonqueens, the chance that the first card selected is not a queen is 4/6. Then if the first card is not a queen, the chance that the second is not a queen is 3/5. Hence, by the rule for the probability of a joint event

The mark has a 0.4 probability of winning \$5 and a 1 – 0.4 = 0.6 probability of losing \$5. Hence, the mark’s expected value in playing the game is
\$5(0.4) + {- \$5)(0.6) = \$2 – \$3 = – \$1
On the average, the mark will lose \$1 per play.

Posted on August 28, 2014 in INTRODUCTION To Statistical Decision Analysis
The text passage contains two distinct mathematical questions, each with a provided answer. The first question involves calculating the expected monetary value of losses for a fire insurance policy, and the second question involves calculating the expected value in a carnival game.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Expected Monetary Value Stats Assignment Homework Help

Expected Monetary Value

When the numbers being averaged are in monetary units, say, United States dollars, expected value is often referred to as expected monetary value and symbolized by EMV. It is computed in the same way as other expected values.
EXAMPLE A fire insurance company assigns a probability of 0.001 that a particular type of building will be completely destroyed by fire during a year, in which case the company will have to pay the insured 100 percent of the value of the building. Similarly, the probabilities of 50 percent and 10 percent damage to the building are, respectively, 0.004 and 0.005. The company classifies all damage as being in one of these three categories. As a first step in determining the amount to be paid for insurance on the building, the company finds the expected monetary value of losses that will 6000 if the building is damaged by fire. The amount to be paid by the buyer of the insurance is called the premium. The premium is larger than the expected loss because the insurance company has to cover expenses and make a profit.The part of the premium which is for expenses and profit is called the loading. (a) If the value of the building is \$80,000, compute the expected value of the loss E(L). (b) If the loading is 30 percent of the premium, compute the premium.
SOLUTION
a. Table 6.2 summarizes the given data and shows the computation of the expected value of the loss E(L) = \$280.
TABLE 6.2
CALCULATING THE EXPECTED LOSS

The difference between the premium, \$400, and the expected loss, \$280, is \$120. Note that \$120is 30 percent of the \$400 premium, as required.
EXERCISE Following the last example, (a) find the expected loss for a  building valued at \$20,000; (b) find the premium if the loading is 25 percent of the premium.
Expected value calculations may involve both gain and loss (negative gain) events.

EXAMPLE In the carnival game of queens, the operator shuffles six cards and places them face down on a table. Two of the cards are kings, two are queens, and two are jacks. The player, called the “mark” in carnival language, selects two cards. The operator bets the mark \$5 even money that at least one of the selected cards is a queen. What is the mark’s expected value in playing this game?

SOLUTION The bet means the mark wins \$5 or loses \$5. The outcomes for the mark are expressed as \$5 and – \$5. The mark wins if neither of the two selected cards is a queen. Because there are 4 nonqueens, the chance that the first card selected is not a queen is 4/6. Then if the first card is not a queen, the chance that the second is not a queen is 3/5. Hence, by the rule for the probability of a joint event

The mark has a 0.4 probability of winning \$5 and a 1 – 0.4 = 0.6 probability of losing \$5. Hence, the mark’s expected value in playing the game is
\$5(0.4) + {- \$5)(0.6) = \$2 – \$3 = – \$1
On the average, the mark will lose \$1 per play.

Posted on August 28, 2014 in INTRODUCTION To Statistical Decision Analysis
user
The text passage contains two distinct mathematical questions, each with a provided answer. The first question involves calculating the expected monetary value of losses for a fire insurance policy, and the second question involves calculating the expected value in a carnival game.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS