A roulette wheel consists of 18 red slots, 18 black slots, and 2 green slots. A player can wager $1 that a marble will land in a red slot, in which case the player would gain a $1. If the marble lands in a slot that isn't
red, then the player loses their $1 wager. Let X represent the player's gain from a random $1 wager on
red. Here's the probability distribution of X along with summary statistics:
Lose
Win
-1
1
X = gain ($)
P(X)
20/38
18/38
Mean:
ux~-$0.05
Standard deviation:
ox~$1.00
Suppose a player decides to wager $5 instead of $1, so the possible outcomes become either losing or
winning $5. Let Z represent the player's gain from a random $5 wager on red.
What are the mean and standard deviation of Z?