 # In this chapter we introduce the idea of a random variable as well as looking at its shape, center, and spread.

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In this chapter we introduce the idea of a random variable as well as looking at its shape, center, and spread.

Let x = the value rolled on a standard 6-sided die. The probability model of x is: xP(x) 1 2 3 4 5 6

You roll a 6-sided die. If it comes up 5 you win \$100. If not you roll again. If it comes up 5, you win \$50. If not, you pay \$20. Let x = amount you “win” when you play this game once. Give the probability model of x.

You roll a 6-sided die. If it comes up 5 you win \$100. If not you roll again. If it comes up 5, you win \$50. If not, you pay \$20. Let x = amount you “win” when you play this game once. Find the mean and the standard deviation of x.

Both the mean and the standard deviation of a random variable can be calculated using our TI 83/84. Put the values of x in L1 and the corresponding probabilities in L2. Then: Here is the calculator screen for the previous example:

A carnival game offers a \$100 cash prize for anyone who can break a balloon by throwing a dart at it from a certain distance. It costs \$5 to play, and you’re willing to spend up to \$20 trying to win, but if you win before spending \$20, you will stop. Let x = the amount you profit from this game, and suppose there is a 10% chance of breaking the balloon on any one throw. Give the distribution of x.

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