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Find , , if a random variable is given by its density function, such that , if , if , if 1. Let be given by its distribution function F(x), such...

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1. Find , ,  if a random variable  is given by its density   function, such that , if   , if  , if  1.  Let  be given by its distribution  function  F(x), such that F(x) = 0   if x   0 F(x) =   if 0<x 2 F(x) =1    if x>2 a) Graph the distribution  function  b) Graph the density  function c) Find ,,  2. A random variable  is distributed normally with E(X) = 8 and  (X) =3 .  Find  σ P(9 X<11).  3. The distribution of the width of a standard piece of computer paper is normal with  an expectation of 8.5 inches and the standard deviation of 0.2 inch. a) Find the probability that the width of any given piece of computer paper is  between 8.40 and 8.55. b) Find the probability that the width of any given piece of computer paper is  less than 8.35. c) Find the probability that the width of any given piece of computer paper is  greater than 8.6. 4. The density function of a random variable  is given by   Find its (a) math expectation, (b) variance and (c) distribution function.   5. Find the density function of a normally distributed random variable, if E(X) = 7.8  and  (X) = 4.1 σ 6. 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). ≤ ≤ ≤ ≤ ≤ ≤ 7. 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?
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1. Find , , if a random variable is given by its density function, such that
, if , if , if We know,
E(X) =
V(X) = 1. Let be given by its distribution function F(x), such that
F(x) = 0 if x ≤...

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