what is the central limit theorem clt and how does it relate to pdfs 
the central limit theorem clt states that the distribution of a random variable in a sample will begin to approach a normal distribution as the sample size becomes larger regardless of the true shape of the distribution thus we know that flipping a coin is a binary process described by the binomial distribution heads or tails however if we consider several coin tosses the odds of getting any particular combination of heads and tails begin to differ for instance if we were to flip the coin 10 times the odds of getting five of each are most likely but getting 10 heads in a row is extremely rare imagine 1 000 coin flips and the distribution approaches the normal bell curve 