If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H) and tails (T). Supposethe random variable X represents the number of heads in a sequence. Construct the probabilitydistribution for X.

The probability distribution of X is:

Step-by-step explanation:

"Tossing a coin and getting H" can be modelled as a Bernoulli random variable. The variable X is a sum of 4 of this Bernoulli variables, we can model X as a binomial random variable, with p=0.5 and n=4.

The values X can take are: 0, 1, 2, 3 and 4.

The values of this probability are calculated as:

Where

p: is the probability of tossing a coin and getting a Heads

q: is the probability of tossing a coin and not getting a Heads.

The binomial number is a way to calculate the possible combinations of getting a certain amount of heads.

For example, in 4 tosses, there are 6 ways or combinations of getting 2 heads and 2 tails: