Probability density functions

Assignment Help Basic Statistics

Reference no: EM13154788

Let { f(x;θ): θ>0} denote a family of probability density functions given by f(x;θ) = Γ(2θ)/(Γ(θ))^2 x^(θ-1) ?(1-x)?^(θ-1), 0<x<1.
a) If a random sample of size 1 is observed, find a UMP(Uniformly Most Powerful) Test of size 0.10 for H0: θ=1 vs Ha: θ>1.
Would you reject Ho if x=0.44 is observed?
b) If a random sample of size 2 is observed, demonstrate that a UMP test of size 0.10 for the above test exists. Also decide the form of the rejection region.

Reference no: EM13154788

Questions Cloud

What is the nash equilibrium price charged by firm : The marginal cost of production is $1.40 to firm 1 and $3.20 to firm 2. The transportation cost is $1 per mile. What is the Nash equilibrium price charged by firm 1? What is the Nash equilibrium price charged by firm 2?

What is the partial pressure of the nitrogen gas : A mixture of O2, CO2, and N2 has a total pressure of 697. torr. In this mixture the partial pressure of O2 is 143. torr and the partial pressure of CO2 is 197. torr. What is the partial pressure of the N2 (in torr)?

What is the objective of accounting standards : A sound foundation is necessary for success in any task from building a house to putting on make-up. In terms of U.S. Accounting Standards, it is also necessary to have a sound foundation, referred to as the conceptual framework. Let's discuss it ste..

Discuss the steps the oligopoly should take to address : Assume that a very competitive start-up enters the market in direct competition with the oligopoly you described in the e-Activity, initially gaining a 12% market share.

Probability density functions : If a random sample of size 2 is observed, demonstrate that a UMP test of size 0.10 for the above test exists. Also decide the form of the rejection region.

Explain what is the annual cost of operation : what is the annual cost of operation in a 70°F room if the door is opened 10 times a day with an average heat gain per opening of 200 kJ? How much would it cost to keep the inside at 35° F

Problem in trading securities : On Jan1, 2009, Nana Co. paid $100,000 for 8000 shares of Papa Co. common stock. These securities were classified as trading securities. The ownership in Papa Co. is 10%.

Becky company began a defined benefit pension plan : Becky Company began a defined benefit pension plan on January 1, 2010. No prior service credit was granted to employees. Service costs amounted to $34,000 in 2010 and $37,000 in 2011. All contributions to the fund were made at the end of the year. At..

Categories of adjusting entries-types of adjustments : Distinguish between the two categories of adjusting entries and identify the types of adjustments applicable to each category

User Account

All Pages