1.2. Learning Objectives#
This week we are covering the binomial distribution and introducing the normal distribution.
You need to understand the following:
1.2.1. 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
1.2.2. 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()