The number of hurricanes that will hit a certain house in the next ten years is Poisson distributed with mean 4. Each hurricane results in a loss that is exponentially distributed with mean 1000. Losses are mutually independent and independent of the number of hurricanes. Calculate

The variance of total loss is 8000000

Step-by-step explanation:

Let

Number of hurricane

Poisson

Loss in each hurricane

Exponential

Total Loss

Required

The variance of the total loss

This is calculated as:

Where:

Expected total loss given X hurricanes

And it is calculated as:

--- Expected Loss in each hurricane * number of loss

Variance of total loss given X hurricanes

And it is calculated as:

---- --- Variance of loss in each hurricane * number of loss

So, we have:

For exponential distribution;

So, we have:

Substitute values

Simplify:

Using variance formula, we have:

For poission distribution:

So, we have:

The expression becomes:

-6 is the correct option from the above given options