math prob
1. Let be given by its distribution function , such that
if
, if 1
, if 2
Find ,,
2. The density function of random variable X is given by the graph below.
Image result for density function graph
a) Find b) Find
3. The density function of a normal random variable is given by.
Find its math expectation and variance
4. A random variable X is normally distributed with the mean 2. The probability that X is between 0 and 2 is 0.35. Find the probability that X is less than 4.
5. A random variable X is normally distributed with the mean 7 and standard deviation 5. Find the probability that X is between 1 and 11. (Use both the Table from Attachment 4 and one of the utilities from Module 6, and compare the results).
2
x
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1
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(
X
E
)
(
X
Var
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(
X
s
(
)
x
r
(
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0.51.5
PX
<<
X
2
(2.5)
18
1
()
32
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-
-
=
X
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x
F
0
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(
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1
x
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=-+