math homework
ProfArgeol
problemset6.docx
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 σ(X) =3 . Find 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 σ(X) = 4.1
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).
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