A Random Variable Distributed

Find  ,  ,   if a random variable   is given by its density  function , such that

f(x)=0, if x≤1

f(x)=3/8 x^2, if 0<x≤2

f(x)=0, if x>2

Let   be given by its distributionfunction  F(x), such that

F(x) = 0 if x ≤ 0

F(x) = x^2/4if 0<x≤2

F(x) =1 if x>2

Graph the distribution function  

Graph the density function

Find  , ,  

A random variable   is distributed normally with E(X) = 8 and σ(X) =3.FindP(9≤X<11).

The distribution of the width of a standard piece of computer paper is normal with an expectation of 8.5 inchesand the standard deviation of 0.2 inch.

Find the probability that thewidth of any given piece of computer paper is between 8.40and 8.55.

Find the probability that the width of any given piece of computer paper is less than 8.35.

Find the probability that the width of any given piece of computer paper is greater than 8.6.

The density function of a random variable   is given by 

f(x)= 1/(7√2π) e^(-〖(x+3.6)〗^2/98)

Find its (a) math expectation, (b) variance and (c) distribution function.

Find the density function of a normally distributed random variable , if E(X) = 7.8 and σ(X) = 4.1

It’s known that a random variable   is distributed normally with   E(X) = 3 and it’s also known  that p(0≤X≤1)+p(5≤X≤6) = 0.6.  Find p(p(5≤X≤6).

Describe a real-life situation to which the normal distribution could be applied. Explain why.  How does a normal distribution differ from one, which is not? Which aspects of your situation might be altered?