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Suppose that the length of time y it takes a worker to complete a certain task has the probability density function given by f (y) = ...where θ is a positive constant that represents the minimum time until task completion Let Y1, Y2, , Yn denote a random sample of completion times from this distribution. (a) Find the density function for Y(1) = min (Y1, Y2, …. ,Yn). (b) Find E(Y(1)). (10%)

Respuesta :

n[ eⁿ(θ - y) is the density function.

What is density in short answer?.

How firmly a material is packed together is determined by its density. As the mass per unit volume, it has that definition.

                        Symbol for density: D or The density is expressed as follows: = m/V, where m is the object's mass and V is its volume.

Let Y₁ , Y₂ .......... Yₙ denoote a random sample of completion times from this distribution .

 min order statistic Y₁ = min ( Y₁ , Y₂ .......... Yₙ )

The density function for y₁ is given by

                          Fy₁ = n[ 1 - F(y)ⁿ⁻¹ f(y)

                             = n[1 - ( 1 - eθ - y)]ⁿ⁻¹  * eθ - y

                           = n[eθ - y]ⁿ⁻¹ * eθ - y

                           = n[ eⁿ(θ - y)

Learn more about density

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