Quiz 7b

Toss a fair, six-sided die.  You win $1 for each spot if there is an odd number of spots.  You lose $1 for each spot if there is an even number of spots.  Give a probability model for your winnings.  Find the expected value and the standard deviation.

You should read "Give  a probability model...." as "Describe the random variable..." because you should notice that we've got (a) an experiment (toss the die) with a random, numerical outcome (win some amount of dollars.)

Let X represent the amount you win.  The the values of X are -6, -4, -2, 1, 3, 5 and their probabilities are
P(X = -6) = P(X = -4) = P(X = -2) = P(X = 1) = P(X = 3) = P(X = 5) = 1/6

E(X) = (1/6)*(-6 -4 -2 + 1 + 3 + 5)  = (1/6) * (-3) = -.5
Don't play this game!  You can expect to lose 50 cents, on average.

Var(X) = (-6 - -.5)^2 *(1/6) + (-4 - -.5)^2 * (1/6) + (-2 - -.5)^2 * (1/6) + (1 - -.5)^2 * (1/6) + (3 - -.5)^2 *(1/6) + (5 - -.5)^2 * (1/6) = 14.917
Sd(X) = sqrt(14.917) = $3.86.

Common mistakes:  Discussing the problem in terms of just "win" or "lose" and ignoring the amount you win or lose.  Using the wrong probabilities.  Although there really wasn't enough time for people to provide me with answers to consider.