Four independent losses, [math]L_1, \ldots, L_4 [/math], are independent and have the following variances:

If loss [math]L_1[/math] and loss [math]L_3[/math] were subject to a common inflation rate while the other two losses aren't, for what level of loss inflation, expressed in %, is the variance of first two losses equal to the last two losses?

• 25%
• 30%
• 50%
• 60%
• 75%

For a constant [math]b = 400[/math], you are given the following about a loss [math]L[/math]:

• [math]\operatorname{E}[L^2 \cdot 1_{L \leq b} ] = 3[/math]
• [math]\operatorname{E}[L \cdot 1_{L \leq b} ] = 2[/math]
• [math]\operatorname{P}(L \leq b) =0.8[/math]

Determine the variance of the loss when a limit of [math]b[/math] is applied.

• 25,276
• 25,279
• 25,603
• 32,003
• 32,103

The random variable [math]X[/math] has a distribution with the following density function:

where [math]\theta [/math] is unknown. If the median of the distribution equals 250, determine the standard deviation of [math]X[/math].

• 19
• 250
• 300
• 361
• 366

A random variable [math]X[/math] has the cumulative distribution function

Calculate the variance of [math]X[/math].

• 7/72
• 1/8
• 5/36
• 4/3
• 23/12

The warranty on a machine specifies that it will be replaced at failure or age 4, whichever occurs first. The machine’s age at failure, [math]X[/math], has density function

Let [math]Y[/math] be the age of the machine at the time of replacement. Calculate the variance of [math]Y[/math].

• 1.3
• 1.4
• 1.7
• 2.1
• 7.5

The distribution of values of the retirement package offered by a company to new employees is modeled by the probability density function

Calculate the variance of the retirement package value for a new employee, given that the value is at least 10.

• 15
• 20
• 25
• 30
• 35

Ten cards from a deck of playing cards are in a box: two diamonds, three spades, and five hearts. Two cards are randomly selected without replacement.

Calculate the variance of the number of diamonds selected, given that no spade is selected.

• 0.24
• 0.28
• 0.32
• 0.34
• 0.41

A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. A tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive). Calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced.

• 208
• 260
• 270
• 312
• 374

A probability distribution of the claim sizes for an auto insurance policy is given in the table below:

Calculate the percentage of claims that are within one standard deviation of the mean claim size.

• 45%
• 55%
• 68%
• 85%
• 100%

An airport purchases an insurance policy to offset costs associated with excessive amounts of snowfall. For every full ten inches of snow in excess of 40 inches during the winter season, the insurer pays the airport 300 up to a policy maximum of 700. The following table shows the probability function for the random variable [math]X[/math] of annual (winter season) snowfall, in inches, at the airport.

Calculate the standard deviation of the amount paid under the policy.

• 134
• 235
• 271
• 313
• 352