The article modeling sediment and water column interactions for hydrophobic pollutants suggests the uniform distribution on the interval (7.5,20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region stats.

1. what is the mean and variance of depth?
2. what is the cdf of depth?
3. what is the probability that observed depth is at most 10? between 10 and 15?
4.what is the probability that the observed depth is within one standard deviation of the mean value? within 2 standard deviations?

1)

2)

3)

4)

Step-by-step explanation:

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability.

Part 1

If X is a random variable that follows an uniform distribution . The mean for an uniform distribution is given by :

On this case a=7.5 and b=20 so if we replace we got:

The variance for the uniform distribution is given by this formula:

And replacing we have:

Part 2

The cumulative distribution function is given by:

Part 3

What is the probability that observed depth is at most 10?

We are interested on this probability:

What is the probability that observed depth is between 10 and 15?

On this case we want this probability:

Part 4

What is the probability that the observed depth is within one standard deviation of the mean value? within 2 standard deviations?

First we find the limits within one deviation from the mean:

And we want this probability:

Now we find the limits within two deviation's from the mean:

But since the random variable is defined just between (7.5 and 20) so we can find just the probability on these limits.

cant open file sorry!

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it