An article suggests the uniform distribution on the interval (7.5, 19) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.

(a) what are the mean and variance of depth? (round your variance to two decimal places.) mean variance

(b) what is the cdf of depth? f(x) = 0 x < 7.5 7.5 ≤ x < 19 1 19 ≤ x

a) Mean: 13.25

Variance: 11.02

b)

0 if x below than 7.5

is x in between 7.5 and 19

1 if x higher than 19.

Step-by-step explanation:

This is a problem in which we use the uniform probability distribution.

(a) What are the mean and variance of depth?

The mean is the midpoint of 7.5 and 19. So

The mean is 13.25

The variance is given by the following formula:

In which b and a are the limits of the interval. So

So

The variance is 11.02.

(b) What is the cdf of depth?

The uniform probability distribution has a cummulative distribution function, of 0 if is below a, for x in between a and b and 1 is x is greater than b.

So:

0 if x below than 7.5

is x in between 7.5 and 19

1 if x higher than 19.

x=30

step-by-step explanation: