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.)

518,400

step-by-step explanation:

the area is multiplying all the given measurements together.

40 * 18 * 30 * 24 = 518,400

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5