6.5.6. Suppose a sufficient statistic exists for the parameter θ. Use Theorem 5.6.1 to show that the critical region of a likelihood ratio test will depend on the sufficient statistic.

Firstly, the defined parameters are X, Q, P,g, h, b

Let X1 = Q1,……..Xn, = Qn be a random sample of size n from the discrete  Px

Step-by-step explanation:

Let X1 = Q1,……..Xn, = Qn be a random sample of size n from the discrete  Px (k;θ) The statistic θ= h(X1,..., Xn) is sufficient for if and only if there are functions g[h(Q1, Qn.);θ]and b(Q1 Qn)   such that L(θ) = g(h(Q1. ..., Qn); ) b(Qi, Qn)  where the function b(QiQn) does not associate  the parameter . A case holds in the continuous case.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204