(Basic Statistics for Citizen Data Scientist) Poisson Distribution Basic Concepts Definition 1: The Poisson distribution has a probability distribution function (pdf) given by The parameter μ is often replaced by λ. A chart of the pdf of the Poisson distribution for λ = 3 is shown in Figure 1.   Figure 1 – Poisson Distribution   Observation: Some key statistical properties of the Poisson …

(Basic Statistics for Citizen Data Scientist) Negative Binomial and Geometric Distributions Negative Binomial Distribution Definition 1: Under the same assumptions as for the binomial distribution, let x be a discrete random variable. The probability density function (pdf) for the negative binomial distribution is the probability of getting x failures before k successes where p = the probability of success on any single trial. Thus …

(Basic Statistics for Citizen Data Scientist) Two-sample Proportion Testing Theorem 1: Let x1 and x2 be random variables with proportional distributions with mean π1 and π2 respectively. Let p1 be the proportion of successes in n1 trials of the first distribution and let p2 be the proportion of successes in n2 trials of the second distribution. When the number of trials n1 and n2 are sufficiently large, usually when ni πi ≥ 5 and ni (1 –πi) ≥ 5, the difference between …

(Basic Statistics for Citizen Data Scientist) One-sample Proportion Testing From the theorem, we know that when sufficiently large samples of size n are taken, the distribution of sample proportions is approximately normal, distributed around the true population proportion mean π, with standard deviation (i.e. the standard error) We can use this fact to do hypothesis testing as was …