three fair coins are tossed simultaneously if x denotes the number of heads find probability distribution of x
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Mean of the probability distribution = ∑(Xi×P(Xi))∑(Xi×P(Xi))
In any coin toss the P(H) = P(T) = 1212
A fair coin is tossed thrice. The sample space of three tosses of a coin is: {HHHTTTHHTTTHHTHTHTHTTTHH}{HHHHHTHTHHTTTTTTTHTHTTHH}
If X is the random variable, we can see that X = 0, 1, 2 or 3 depending on the # of heads.
P (X = 0) = P (no heads) = P (TTT) = 1818
P (X = 1) = P (HTT, TTH and THT) = 3838
P (X = 2) = P (HHT, HTH and THH) = 3838
P (X = 3) = P (HHH) = 1818
Therefore, given this probability distribution we can calculate the mean using the formula Mean of the probability distribution = ∑(Xi×P(Xi))∑(Xi×P(Xi))
⇒⇒ Mean =0×18=0×18 +1×38+1×38 +2×38+2×38 +3×18=128=32
In any coin toss the P(H) = P(T) = 1212
A fair coin is tossed thrice. The sample space of three tosses of a coin is: {HHHTTTHHTTTHHTHTHTHTTTHH}{HHHHHTHTHHTTTTTTTHTHTTHH}
If X is the random variable, we can see that X = 0, 1, 2 or 3 depending on the # of heads.
P (X = 0) = P (no heads) = P (TTT) = 1818
P (X = 1) = P (HTT, TTH and THT) = 3838
P (X = 2) = P (HHT, HTH and THH) = 3838
P (X = 3) = P (HHH) = 1818
Therefore, given this probability distribution we can calculate the mean using the formula Mean of the probability distribution = ∑(Xi×P(Xi))∑(Xi×P(Xi))
⇒⇒ Mean =0×18=0×18 +1×38+1×38 +2×38+2×38 +3×18=128=32
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