Printer Failure The lifetime of a printer costing 200 is...

Printer Failure The lifetime of a printer costing $\$ 200$ is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a onc-half refund if it fails during the second year. If the manufacturer sells 100 printers, how much should it expect to pay in refunds? Choose one of the following. Source: Society of Actuaries. $$ \begin{array}{lllllllll}{\text { a. } 6321} & {\text { b. } 7358} & {\text { c. } 7869} & {\text { d. } 10,256} & {\text { e. } 12,642}\end{array} $$

Printer Failure The lifetime of a printer costing $\$ 200$ is exponentially distributed with mean 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a onc-half refund if it fails during the second year. If the manufacturer sells 100
printers, how much should it expect to pay in refunds? Choose one of the following. Source: Society of Actuaries.
$$
\begin{array}{lllllllll}{\text { a. } 6321} & {\text { b. } 7358} & {\text { c. } 7869} & {\text { d. } 10,256} & {\text { e. } 12,642}\end{array}
$$

Key Concepts

Expected Value

The concept of expected value involves computing the average outcome of a random variable, taking into account all possible outcomes weighted by their probabilities. In risk or cost predictions, such as determining expected warranty refunds, it provides a crucial measure for long-term planning and decision making.

Conditional Probability

Conditional probability refers to the calculation of probabilities for events that depend on the occurrence of other events. When payout conditions change based on different time intervals (e.g., full refund in one period and half refund in a later period), conditional probability helps in determining the chance of each scenario.

Exponential Distribution

The exponential distribution models the time until an event occurs, such as equipment failure, with a constant failure rate over time. It is memoryless, meaning that the probability of failure in the next moment is independent of how long the equipment has already lasted. This property makes it a popular choice in reliability and survival analysis.

Actuarial Analysis

Actuarial analysis applies statistical and mathematical techniques to assess and manage risk in various industries, including insurance and finance. It involves forecasting future payments and liabilities by considering probabilities of events and their financial impacts, which is essential in evaluating warranty and refund policies.

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