A random sample of size n is to be used to test the null hypothesis that the parameter θ of an exponential population equals θ0 against the alternative that it does not equal θ0. (a) Find an expression for the likelihood ratio statistic. (Note that, the ML estimator of the parameter θ of an exponential distribution is X.) (b) Use the result of Part (a) to show that the critical region of the likelihood ratio test can be written as xe−x/θ0 ≤ K.

Create and solve a linear equation that represents the model, where squares and triangles are shown evenly balanced on a balance beam. assume the weight of a square is 1 unit and the weight of a triangle is unknown.

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?

What is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83