Question

An article suggests the uniform distribution on the interval (6.5, 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

Answer 1

Answer:

The mean of depth is 12.75cm.

The variance of depth is of 13.02 cm².

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

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

The variance of the uniform distribution is given by:

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

Uniform distribution on the interval (6.5, 19)

This means that: $a = 6.5, b = 19$

So

Mean:

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

The mean of depth is 12.75cm.

Variance:

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

The variance of depth is of 13.02 cm².