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Find the mean number of heads in three tosses of a fair coin.
Given: A coin is tossed three times.
three coins are tossed simultaneously. Hence, the sample space of the experiment is S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
X represents the number of heads.
As we see, X is a function on sample space whose range is {0, 1, 2, 3}.
Thus, X is a random variable which can take the values 0, 1, 2 or 3.
P(X = 0) = P(TTT)
P(X = 1) = P(TTH) + P(THT) + P(HTT)
P(X = 2) = P(THH) + P(HTH) + P(HHT)
P(X = 3) = P(HHH)
Hence, the required probability distribution is,
X | 0 | 1 | 2 | 3 |
P(X) |
Therefore mean μ is:
A random variable X has the following probability distribution:
X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
P(X) | 0 | k | 2k | 2k | 3k | K2 | 2 K2 | 7 K2 + k |
Determine
(i) k (ii) P(X < 3)
(iii) P(X > 6) (iv) P(0 < X < 3)