Assume we have n = 20 i. i.d. observations x1, x2, xn from the exponential distribution with rate parameter λ. we want to test h0 : λ ≤ 8 vs. ha : λ > 8. develop a uniformly most powerful α = 0.05 level test and derive the rejection region of this test. (hint: when xi , 1 ≤ i ≤ n independently follows an exponential distribution of rate λ, then x : = pn i=1 xi ∼ gamma(n, λ), which has the density λ n γ(n) x n−1 e −λx, x > 0. use the quantile function shape = rate = lower. tail = in r to compute the cutoff value.)

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation:

1st part is 64,000,000

2nd part 500,000

step-by-step explanation:

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.

the area of a triangle is determined by the formula: base x height * 1/2

you'll need to assign a base to the triangle. based on the vertices given, the simplest base would be the line segment from (-2,1) to (2,1). the distance between any two numbers is found by just subtracting them. here, you should subtract the x values to find the distance of this side.

2 - (-2) = 4.

so the distance (aka the length of the base) is 4. the height of the triangle is the distance between the base and the highest point on the triangle which is (3,4). we should subtract the y values this time to find the height/distance.

4 - 1 = 3

so the height is 3.

base = 4

height = 3

hope this if needed hmu