Expected Value

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 probabilitydistribution has an expected value (mean) of 54 and a standard deviationof 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. …

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.