Figure 1. Schematic notation of random variables and probability distribution functions for statistical analysis.

A heterogeneous solution of target and non-target cells is loaded to a droplet ejector. (a) Random cell encapsulation process. (b) Three random variables and one dependent variable were mapped to a patterned array of cell encapsulating droplets which represents number of droplets that contain cells, number of cells per droplet, number of target cells, and droplets encapsulating a single target cell, respectively. The probability of the process can be described as (c) binomial distribution, which represents success and failure corresponding to cell containing and empty droplets, respectively. (d) Poisson distribution is used for the random variable, X_c, since the number of cells per droplet is the count of occurrence of a rare event (i.e., probability of the event is very low) in probability space with respect to the number of sampled droplets and droplet volume. (e) Overall system random process becomes the combined function of suggested PDFs. The PDFs for the random variables, X_d and X_c, are used for the overall PDF of the system. The parameter λ represents the Poisson coefficient, and μ, and σ represent mean, and variance of the underlying probability distributions, respectively. All distribution functions were interpolated to a continuous curve with colored bars on graph indicating the discrete values.