Question4: A game consists of tossing two coins, first a dime and then a nickel.

Question

Question4: A game consists of tossing two coins, first a dime and then a nickel. For each coin which comes up a head you win the value of the coin. For each coin which comes up a tail you get nothing. 1) List the possible outcomes, in terms of heads and tails, and give the probability and your winnings for each outcome. TH,T each outsome has probability .5 winnings are 5 and0 HH,HT,TH,TT each outcome with probability .25 winnings are 10,5,5,o HH,HT,TH,TT) each outcome with probability .25- winnings are 15,5,10,0 HH,HT,TH,TT) each outcome with probability .25- winnings are 15,10,5,0 Tries 0/2 2) Find the mean or expected winnings. 2.5 7.5 10 . Tries 1/2 3) Find the standard deviation 31.25 37.5 6.12 5.59 Tries 0/2 4) If you had to pay a dime to play the game, what would be the mean of your winnings? 7.5 2.5 2.5 7.5 10 Tries 0/2 5) If you had to pay a dime to play the game, what would be the standard deviation of your winnings? 5.59 6.12 31.25 37.5 Tries 0/2

Explanation / Answer

1) Option-D)

2) Mean, E(X) = 0.25 * (15 + 10 + 5 + 0) = 7.5

Option-C) 7.5

3) E(X2) = 0.25 * (152 + 102 + 52 + 02) = 87.5

Var(X) = E(X2) - (E(X))2 = 87.5 - 7.52 = 31.25

Standard deviation = sqrt(31.25) = 5.59

Option-D) 5.59

4) Option-G) 7.5

5) Option-A) 5.59

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