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Expected Value problems
Expected Value example question
A box contains 8 green and 4 blue marbles. Two marbles are selected at once without replacement. What is the expected number of green marbles among the selected ones?
a) 1
b) 
c) 
d) 
e) 
f) none of the above
Solution to this Expected Value practice problem is given in the video below!
Expected Value example problem #2
You have 5 pairs of shoes. Four of them are worth $30 each, while the fifth is worth $2,000. You select a pair at random. What is the expected value of the pair you have selected?
a) $424
b) $30
c) $50.20
d) $432
e) $1,030
f) none of the above
Solution to this Expected Value practice problem is given in the video below!
Binomial Distribution Expectation example
A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.
Solution to this Binomial Random Variable Expected Value practice problem is given in the video below!
Hypergeometric Distribution Expectation example question
A ball is chosen at random from each of 5 urns. Each urn contains balls as follows:
urn 1: 1 white, 5 black
urn 2: 3 white, 3 black
urn 3: 6 white, 4 black
urn 4: 2 white, 6 black
urn 5: 3 white, 7 black
Compute the expected number of white balls selected.
Solution to this Hypergeometric Random Variable Expected Value practice problem is given in the video below!
Continuous Distribution Expected Value example problem
The density function of X is given by
f(x) = { 
0 otherwise
If E[X] = 
, find the values of constants 
and 
.
Solution to this Continuous Random Variable Expected Value practice problem is given in the video below!
Independent & Identically Distributed UNIFORM Random Variables Expected Value example
If X1, X2, …, Xn are independent and identically distributed random variables having uniform distributions over (0,1),
find
E [max(X1, …, Xn)]
and
E [min(X1, …,Xn)]
Solution to this Uniform Random Variable Expected Value practice problem is given in the video below!
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