contestada

An actuary was analyzing the loss experienced by flooding on houses and concluded that it was uniformly distributed on [0, 1000]. After taking another look at the data, he realized the loss amounts used were in real dollars. He then determined that the inflation rate was at 6.5%. Assume that the rest of his analysis still holds true. Calculate the probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.

Respuesta :

Answer:

100%  probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniformly distributed on [0, 1000].

This means that [tex]a = 0, b = 1000[/tex]

Given that the loss in nominal dollars is greater than 200.

This means that [tex]a = 200[/tex]

Calculate the probability that the loss in nominal dollars is less than 1000

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

[tex]P(X < 1000) = \frac{1000 - 200}{1000 - 200} = 1[/tex]

100%  probability that the loss in nominal dollars is less than 1000, given that the loss in nominal dollars is greater than 200.

Otras preguntas