I have a question regarding an experiment where 5 fair coins are flipped, but the random variable has a quirk and is throwing me off. Fair in this case means the probability of success is p = 0.5
Each coin is labeled with +1
on the heads side and -1
on the tails side. If the random variable X is the sum of the outward facing labels after each coin is flipped, then X({HHTTH}) = 1+1-1-1+1 = 1`.
What is the probability mass function of the random variable X
?
I need the pmf in order to calculate the mean, variance, and standard deviation, but I've become used to X being the number of successes, where tails is labeled 0
but in this problem, tails is marked -1
.
My attempt at solving this would be to represent each coin as an independent Bernoulli trial, leading to the number of successes following a binomial distribution, but this doesn't accurately represent the random variable. Any help would be immensely appreciated.