Suppose x and y are random variables with joint density function. f(x, y) = 0.1e−(0.5x + 0.2y) if x ≥ 0, y ≥ 0 0 otherwise (a) is f a joint density function? yes no (b) find p(y ≥ 8). (round your answer to four decimal places.) find p(x ≤ 5, y ≤ 8). (round your answer to four decimal places.) (c) find the expected value of x. find the expected value of y.

a. is a joint density function if its integral over the given support is 1:

so the answer is yes.

b. We should first find the density of the marginal distribution, :

Then

or about 0.2019.

For the other probability, we can use the joint PDF directly:

which is about 0.7326.

c. We already know the PDF for , so we just integrate:

we'll this would mean that the dunk tank and the bounce house are the same for 20 hours because the 2 represents that the two activities, and the 20 represents the amount of hours they both are. so with this said, it means that the answer is c. the costs for a dunk tank and bounce house are the same for 20 hours.

c.the costs for a dunk tank and bounce house are the same for 20 hours.

hope this .

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.