Statistics

1. Consider the experiment of tossing a fair coin five times. If we let X = the number of times the coin lands on tails than X is a random variable. Find the expected value, variance, and standard deviation for X

2. A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $2 to play the game and the winning price is $6. Mathematicaly analyze this game and determine if it is in your financial interest to play the game.