Question -
Answer -
Given a coin is tossedthree times.
Three coins are tossedsimultaneously. Hence, the sample space of the experiment is S = {HHH, HHT,HTH, THH, TTH, THT, HTT, TTT}
X represents thenumber of heads.
As we see, X is afunction on sample space whose range is {0, 1, 2, 3}.
Thus, X is a randomvariable which can take the values 0, 1, 2 or 3.
P (X = 0) = P(TTT) = 1/8
P (X = 1) = P (TTH) +P (THT) + P (HTT) = 1/8 +1/8 + 1/8 = 3/8
P (X = 2) = P (THH) +P (HTH) + P (HHT) = 1/8 + 1/8 + 1/8 = 3/8
P (X = 3) = P (HHH) =1/8
Hence, the requiredprobability distribution is,
| X | 0 | 1 | 2 | 3 |
| P (X) | 1/8 | 3/8 | 3/8 | 1/8 |
Therefore mean μ is:
