Answer to Question #258388 in Statistics and Probability for cluezmbtch

Question

Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z.

Answer 1

Since 4 coins are tossed, then there are 5 values that variable Z might take (from 0 to 4)

Z has binomial distribution Bin(4*0.5, 4*0.5*0.5) = Bin(2, 1)

$P(Z = n) = {4 \choose n}*0.5^{n}*0.5^{4-n}={4 \choose n}*0.5^4$

The probabilities of taking each value are presented in a table below