Answer to Question #330682 in Statistics and Probability for BEN

Question #330682

Four coins are tossed at once. Let Y be the random variable representing the number of

heads that occur.



1
Expert's answer
2022-04-21T04:02:25-0400

Let XiX_i = 1, if head occur for coin i else 0, then XiX_i is distributed according to Bernoulli distribution with parameter p = 0.5 (because coins are symmetrical)

Then Y=i=14XiY = \sum_{i=1}^4 X_i is distributed according to Binomial distribution with parameters p = 0.5 and n = 4.


Then possible values of Y: {0, 1, 2, 3, 4}


Probability distribution of Binomial distribution:

Pr(Y=k)=Cnkpk(1p)nk=4!(4k)!k!(12)4Pr(Y=k) = C_n^k p^k (1-p)^{n-k} = \frac{4!}{(4-k)!k!}(\frac{1}{2})^4

Pr(Y=0) = 0.0625

Pr(Y=1) = 0.25

Pr(Y=2) = 0.375

Pr(Y=3) = 0.25

Pr(Y=4) = 0.0625



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