Annual windstorm losses, X and Y, in two different regions are independent, and each is uniformly distributed on the interval [0, 10]. Calculate the covariance of X and Y, given that X+ Y < 10.

Step-by-step explanation:

Given

Required

First, we calculate the joint distribution of X and Y

Plot

So, the joint pdf is:

--- i.e. the area of the shaded region

The shaded area is a triangle that has: height = 10; width = 10

So, we have:

is calculated as:

Calculate E(XY)

Make Y the subject

So, we have:

Rewrite as:

Integrate Y

Expand

Rewrite as:

Expand

Integrate

Expand

Take LCM

Calculate E(X)

Rewrite as:

Integrate Y

Expand

Integrate

Expand

Take LCM

Calculate E(Y)

Rewrite as:

Integrate Y

Expand

Rewrite as:

Integrate

Expand

Recall that:

Take LCM

i think is 3 and 6. this took me 10 min to think.hope to and hope that my answer is brainliest.(follow me )

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