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# Tag Archives: probability expectation example solutions

## 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!