During one holiday season, the Texas lottery played a game called the Stocking Stuffer.

With this game, total instant winnings of $34.8 million were available in 70 million $1 tickets, with ticket prizes ranging from $1 to $1,000. Shown here are the various prizes and the probability of winning each prize. Use these data to compute the expected value of the game, the variance of the game, and the standard deviation of the game. (Remark: this mean, variance, and standard deviation is not the same as the sample).

PRIZE (x)………………………………….PROBABILITY P(x)

$1,000……………………………………………...00002

100…………………………………………………..00063

20…………………………………………………….00400

10…………………………………………………….00601

4……………………………………………………...02403

2……………………………………………………..08877

1……………………………………………………..10479

0……………………………………………………..77175