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An insurance policy sells for $600. Based on past data, an average of 1 in 50 policy holders
will file a $5,000 claim, an average of 1 in 100 policyholders will file a $10,000 claim, and an average
of 1 in 200 policyholders will file a $30,000 claim.
(a) Find the expected value (to the company) per policy sold.
(b) If the company sells 10,000 policies, what is the expected profit or loss?

Respuesta :

Using the expected value of a discrete distribution, the values are given as follows:

a) $250.

b) $2,500,000.

What is the mean of a discrete distribution?

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

The distribution of the company's earnings is given as follows:

  • P(X = -4400) = 0.02.
  • P(X = -9400) = 0.01.
  • P(X = -29400) = 0.005.
  • P(X = 600) = 0.965.

Considering that the policy sells for $600, for example, a $5000 claim is a loss of $5000 - $600 = $4,400 for the company, which explains the above distribution.

Item a:

The expected value for a policy sold is given by:

E(X) = 600(0.965) - 4400(0.02) -9400(0.01) - 29400(0.005) = 250.

Item b:

Considering the value found in item a for a single policy, for 10,000 policies, the expected profit is given by:

E = 10000 x 250 = 2,500,000.

More can be learned about discrete distributions at https://brainly.com/question/24802582

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