Learning Objectives

2.2. Learning Objectives#

This week we are covering the binomial distribution and introducing the normal distribution.

You need to understand the following:

2.2.1. Conceptual#

Binomial#

  • What types of data are binomially distributed

  • Formulae for the mean and variance of binomial

  • How to calculate the probability of exactly k hits out of n trials (using the PMF)

  • How to calculate the probability of at least k hits out of n trials (using the CDF)

  • How to fit a normal approximation to a binomial for given n,p

  • When the Normal approximation is appropriate

Normal#

  • For a normally distributed variable x~N(m,s), calculate the probability that x falls in a given range, using the CDF

  • Convert values of x into Z-scores

  • Understand the relationship of the normal to the binomial distribution

2.2.2. Python skills#

  • How to simulate a binomial trial (one value of k, when k~B(n,p), using np.random.binomial()

  • How to simulate data from a normal distribution (one value of x, when x~N(m,s), using np.random.normal()

  • How to obtain the PMF of the binomial for a given value of k using stats.binom.pmf()

  • How to obtain the PDF of the normal for a given value of x using stats.norm.pdf()

  • How to obtain the CDF of the binomial for a given value of k using stats.binom.CDF()

  • How to obtain the CDF of the normal for a given value of x using stats.norm.CDF()

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