Question

Consider a simple experiment that involves flipping a coin 8 times and recording the number of heads. We’ll suppose that this experiment has been performed many times, and we’ll look to see whether the results are consistent with the coin being fair. Define the random variable X to be the number of heads observed in 8 flips of the coin.

Q1: If the coin is fair, what is the distribution of X? Name it and give the values of the parameters.

Answer 1

Random variable X is Binomially distributed.

it is a binomial probability distribution, because there is fixed number of trials,
only two outcomes are there, success and failure
trails are independent of each other

where, parameters are

Sample size , n =    8
Probability of an event of interest, (head) p =   0.50

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Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

X	P(X)
0	0.0039
1	0.0313
2	0.1094
3	0.2188
4	0.2734
5	0.2188
6	0.1094
7	0.0313
8	0.0039