Exam P Practice Question 4

Study guide: Exam P-1

A loss $X$ is uniformly distributed on the interval $(0, 1{,}000)$ . An insurance policy pays the amount of the loss in excess of a deductible of 200, up to a maximum payment of 500. Let $Y$ be the payment, so

$Y = \min\big(\max(X - 200,\ 0),\ 500\big).$

Which of the following statements about the random variable $Y$ is true?

A) $Y$ is mixed: it has probability 0.2 at 0, probability 0.3 at 500, and a density in between
B) $Y$ is continuous, since it is a function of the continuous loss $X$ and can take any value in $[0, 500]$
C) $Y$ is discrete, since its distribution function has jumps, which a continuous random variable cannot have
D) $Y$ is mixed: it has probability 0.2 at 0, and its distribution function has no jump at 500
E) $Y$ is mixed: it has probability 0.2 at 0, probability 0.5 at 500, and a density in between

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Concepts tested

Random Variable
Payment Random Variable
Continuous Random Variable
Discrete Random Variable
Cumulative Distribution Function (CDF)
Deductible
Benefit Limit

Exam P Practice Question 4

Concepts tested

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