Question 871484: A fair coin is flipped two independent times. Suppose the Random Variables X1,X2 where:
Xi={1, Heads in i toss,
___{0, Tails in i toss}
for i=1,2.
Count the domain, the mass, the function of probability, the mean, the dispersion for the R.V. Y = 2X1, Z = X1+X2, W=1-X1+X2 .
Having answered on the above questions, which one of the two following games would you play. (Justify your answer.)
(i) Game 1: You throw a coin and you earn 2 Euros if "Heads" is the outcome.
(ii) Game 2: You throw two coins and you earn 1 Euro for every coin for which "Heads" is the outcome.
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
thoughts on this one.
A fair coin is flipped two independent times
SS P RV value
HH 1/4 2
HT 1/4 1
TH 1/4 1
TT 1/4 0
E = 2(1/4) + 1(1/4) + 1(1/4) + 0(1/4) = 1 Perhaps this is what You are Looking for.
P(x=0) 1/4
P(x =1) 2/4
P(x= 2) 1/4
Mass function = 2Cx/4 for x = 0,1,2
(i) Game 1: You throw a coin and you earn 2 Euros if "Heads" is the outcome.
E = (1/2)2Euro = 1Euro
(ii) Game 2: You throw two coins and you earn 1 Euro for every coin for which "Heads" is the outcome.
E = (3/4)1Euro = .75 Euro
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