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Let be the bivariate normal pdf in expression (3.5.1). (a) Show that has an unique maximum at (b) For a given c > 0, show that the points of equal probability form an ellipse.

For the Burr distribution, show that provided 

Prepare a financial plan for the company you select for your business plan. This financial plan will be included in your final business plan in your capstone course. Describe the business, including the type of business. Create the business case. Determine why funding is needed for the company. Determine the sources of funding. Considerself-funding, borrowing,

Let the number X of accidents have a Poisson distribution with mean . Suppose λ, the liability to have an accident, has, given θ, a gamma pdf with parameters α = h and ; and θ, an accident proneness factor, has a generalized Pareto pdf with parameters α, λ = h, and k. Show that the unconditional

Let X have a conditional Burr distribution with fixed parameters β and τ, given parameter α.

6-8 page (APA style) reflection paper. Your paper answers the question:  What leadership lessons have you gleaned from this course, how does it relate to your work/life setting, and what practical applications will be implementing?  Refer to the book （Lead Like Jesus Revisited: Lessons from the greatest leadership role model of all time. or The

1. Let  have the conditional Weibull pdf and let the pdf (weighting function)  be gamma with parameters α and β. Show that the compound (marginal) pdf of X is that of Burr.

2. If X has a Pareto distribution with parameters α and β and if c is a positive constant, show that  has a Pareto distribution with parameters α and .

Choose an organization (or use your own) and create a crisis communication plan. Your plan should include the following parts: Introduction & Table of Contents Brief organization background to serve as information for crisis management team Description of the Plan’s Purpose, including its Identify types of crises your organization could face (categorize these under broad

Twenty motors were put on test under a high-temperature setting. The lifetimes in hours of the motors under these conditions are given below. Also, the data are in the file lifetimemotor.rda at the site listed in the Preface. Suppose we assume that the lifetime of a motor under these conditions, X, has a Γ(1, θ)