From the Swirl() class of statistical inference on common distributions.
- A Bernouilli random variable (B_RV) takes only 1 and 0 with p and 1-p respectively.
- E(B_RV) = p
- Var(B_RV) = p(1-p) (from Var(RV) = E(RV^2) - E(RV)^2)
- a binomial RV are sums of Bernouilli trials (RV). biRV = B_RV1 + B_RV2 + …._ B_RVn (all B_RV are iid, independent and identically distributed)
So for us who analyse how many cells with a Ape1 dot have this Ape1 dot at the vacuole. For each cell with an Ape1 dot, this is a Bernouilli trial, yes or no. We look at different cells of each strain and since we treat generally all strains and cells the same, we can for each strain say
- the number of cells with Ape1 dots at which the dot is at the Vacuole is a Binomial Random Variable (the outcome of an experiment) = biRV
- The biRV gives us the number of successes x out of n iid Bernouilli trials (with success rate = p)
- the PMF (probability mass function) is:
\[P(biRV = x) = {n \choose x} p^{x} * (1-p)^{n-x}\]
- We are then interested in whether p is significantly different for the different strains.