tossing a coin three times , define the random variable X on S where X is the number of heads for each tossing and calculate the probability mass function.

tossing a coin three times , define the random variable X on S where X is the number of heads for each tossing and calculate the probability mass function.

S={HHH,HTH,HHT,THH,HTT,THT,TTH,TTT} N(S)=8 X={0,1,2,3} Which is a discrete r.v. P(X=0)=P{TTT}=1/8 P(X=1)=P{HTT,THT,TTH}=3/8 P(X=2)=P{HHT,HTH,THH}=3/8 P(X=3)=P{HHH}=1/8 This can be written in the following table:

S={HHH,HTH,HHT,THH,HTT,THT,TTH,TTT}

N(S)=8

X={0,1,2,3} Which is a discrete r.v.

P(X=0)=P{TTT}=1/8

P(X=1)=P{HTT,THT,TTH}=3/8

P(X=2)=P{HHT,HTH,THH}=3/8

P(X=3)=P{HHH}=1/8

This can be written in the following table:

3210x1/83/83/81/8p(x)