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(A) Show That p(x)={(2k)x3+k if x10 otherwise p ( x ) = \left\{ \begin{array} { l l } ( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \\0 & \text { otherwise }\end{array} \right.

question 182

Essay

(a) Show that p(x)={(2k)x3+k if x10 otherwise p ( x ) = \left\{ \begin{array} { l l } ( 2 - k ) x ^ { - 3 + k } & \text { if } x \geq 1 \\0 & \text { otherwise }\end{array} \right. where k is fixed and 0<k<10 < k < 1 is a probability density function.(b) What is the mean for this distribution?
(c) Calculate the median of pp


Definitions:

Isotonic Solution

A solution that has the same osmotic pressure as another solution, typically referring to body fluids.

Phospholipid Bilayer

The fundamental structure of cellular membranes, consisting of two layers of phospholipids with hydrophilic heads facing outwards and hydrophobic tails facing inwards.

Membrane Channel Protein

Proteins that form pores in the cell membrane, allowing specific ions or molecules to pass through.

Internal Membrane Surface

The side of a membrane that faces towards the interior of the cellular organelle or structure it surrounds.

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