Use the table above to determine P(X is greater than or equal to 2). Determine the expected value of X.
PROBLEM 2

Two fair dice are tossed. You bet $5 that you will roll "an even sum". If you roll "an even sum" you win $10. Otherwise you lose the $5 bet. What is the expected return on this game?
PROBLEM 3

Two fair dice are tossed. You bet $1 that you will roll "doubles". If you roll "doubles" you win $60. Otherwise you lose the $1 bet. What is the expected return on this game?

PROBLEM 4

A probability distribution has an expected value (mean) of 54 and a standard deviation of 0.7. Use Chebyshev's inequality to find the minimum probability that an outcome is between 40 and 68.

I've put explanations in with the Word document. See the attached file.

PROBLEM 1

Random variable X 0 1 2 3
P (X=x) .125 .375 .250 .250

Use the table above to determine P(X is greater than or equal to 2). Determine the expected value of X.

So looking at the table, P(X>=2) = P(X=2) + P(X=3)
Since these are the only possible values of X that are equal to or greater than (>=) 2.
The table tells us the probabilities of X=2 and X=3 are each 0.25.
Therefore, P(X>=2) = 0.5

The expected value of a random variable is defined as the sum of

x P(X=x) = (0 x 0.125) + (1 x 0.375) + (2 x 0.25) + (3 x 0.25) = 1.625

PROBLEM 2

Two fair dice are tossed. You bet $5 that you will roll "an even sum". If you roll "an even sum" you win $10. ...

Solution Summary

A probability distribution has an expected value (mean) of 54 and a standard deviation of 0.7 are calculated. The Chebyshev's inequality is used to find the minimum probability that an outcome is between 40 and 68.

An investment of $20 in Stock A is expected to pay no dividends and have value of $24 in 1 year. An investment of $70 in Stock B is expected to generate a $2.50 dividend next year and price of its stock is expected to be $78.
1) What are the expected returns
2) If the required return is 10%, which
stock(s) should be profit

Risk free rate of 7% and market risk premium of 2 %. The best investment of these:
Expected Return of 9.01 / Beta 1.70
Expected Return of 7.06 / Beta 0.00
Expected Return of 5.04 / Beta -0.67
Expected Return of 8.74 / Beta 0.87
Expected Return of 11.50 / Beta 2.50
The 7.06 with Beta of 0.00 is best, but how do I calculat

Properties of ExpectedValues
Attached is a Adobe pdf file. I am studying for a test and wish to use this problem as a guide. Please give as much detail as possible so that I may understand the concept.

Let X be a random variable having expectedvalue (mu) and variance (sigma)^2. Find the expectedvalue and variance of:
Y = (X - mu)/(sigma).
(See attachment for full question)

Expected payoff corresponding to various levels of business expansion and economic conditions faced by Ramcast Cable Inc. is given in the table below. The probabilities of the events are also given. What is each expected monetary value (EV) of each alternative below, and the maximum expected monetary value (EV) in the payoff mat

You have invested in a project that has the following payoff schedule:
Payoff Probability of Occurrence
$40 .15
$50 .20
$60 .30
$70 .30
$80 .05
What is the expectedvalue of the investment's payoff? (Round to the nearest $1)
A) $70
B) $60
C) $59
D) $65

Suppose the tax rate is 30% if taxable income Is positive and 0%, if taxable income is negative, Calculate the expected tax payable for the following four projects. Note that for each project the expected taxable income is $50,000. For each project, also calculate the expected average tax rate (expected total taxes divided by

The Ramshead Pub sells a large quantity of beer every Saturday. From the past sales records the pub has determined the following probabilities for sales. Compute the expected number of barrels that will be sold on Saturday.
Barrels Probability
6 .10
7