5.2. Learning Objectives#
This week we are covering the binomial distribution and introducing the normal distribution.
You need to understand the following:
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, including continuity correction
- 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 distriubtion
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 ofxk 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 ofxk using stats.norm.CDF()