Question

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is: Compute E(Y) Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is:

y | P(Y)

0 | 0.50

1 | 0.20

2 | 0.25

3 | 0.05

Compute E(Y)

Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.

Answer:

The expected value E(Y) is

`E(Y) = 0.85`

The expected amount of the surcharge is

`E(100Y^2) = 165`

Explanation:

Let Y be the number of moving violations for which the individual was cited during the last 3 years.

The given probability mass function (pmf) of Y is

y | P(Y)

0 | 0.50

1 | 0.20

2 | 0.25

3 | 0.05

Compute E(Y)

The expected value E(Y) is given by

`E(Y) = \sum Y \cdot P(Y) \\\\E(Y) = 0 \cdot 0.50 + 1 \cdot 0.20 + 2 \cdot 0.25 + 3 \cdot 0.05 \\\\E(Y) = 0.85`

Suppose an individual with Y violations incurs a surcharge of $100Y2. Calculate the expected amount of the surcharge.

The expected amount of the surcharge is given by

`E(100Y^2) = 100E(Y^2)`

Where

`E(Y^2) = \sum Y^2 \cdot P(Y) \\\\E(Y^2) = 0^2 \cdot 0.50 + 1^2 \cdot 0.20 + 2^2 \cdot 0.25 + 3^2 \cdot 0.05\\\\E(Y^2) = 1.65`

So, the expected amount of the surcharge is

`E(100Y^2) = 100E(Y^2) \\\\E(100Y^2) = 100 \cdot 1.65 \\\\E(100Y^2) = 165`