An article suggests the uniform distribution on the interval (6.5, 19) as a model for depth (cm) of the bioturbation layer in se

Question

1 month ago

12

diment in a certain region.(a) What are the mean and variance of depth

1 answer:

tester [12.3K] · Answer 1 · 2026-04-09T03:10:38+03:00

Response:

The average depth is 12.75 cm.

The depth variance is calculated as 13.02 cm².

Clarification:

Uniform probability occurs when every outcome is equally probable.

In this scenario, we have a lower limit of the distribution denoted as a and an upper limit referred to as b.

The mean of the uniform distribution is:

$M = \frac{a+b}{2}$

The variance of the uniform distribution is represented as:

$V = \frac{(b-a)^{2}}{12}$

Uniform distribution across the interval (6.5, 19)

Thus, we have: $a = 6.5, b = 19$

So

Mean:

$M = \frac{6.5+19}{2} = 12.75$

Average depth is 12.75cm.

Variance:

$V = \frac{(19 - 6.5)^{2}}{12} = 13.02$

The variance of depth equals 13.02 cm².