SOLUTION: 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

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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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