Final Exam: Statistics and Probability

WHAT YOU WILL LEARN

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  Describe what statistics, populations, and samples are
  

  recognize how metrics such as mean, median and mode describe data
  

  summarize the workings a number of probability sampling techniques
  

  load data from a csv file into a pandas dataframe and perform some initial analysis
  

  calculate the mean and median of a distribution using your own function and compare it with the built-in pandas function
  

  use seaborn and matplotlib to visualize a distribution and where the mean, median, and mode fit in
  

  calculate the mean and median of a distribution using your own function and compare it with the built-in pandas function
  

  create a balanced sample using random undersampling and oversampling
  

  define terms such as event, outcome, and experiment
  

  import python libraries needed to work with probabilities
  

  simulate the flipping of a coin in python
  

  define joint, marginal, and conditional probability
  

  simulate the rolling of two die to test joint probability
  

  calculate joint probabilities associated with the rolling of a die
  

  calculate the joint probability of dependent variables
  

  define the formula of the expected value of a random variable
  

  compute conditional probabilities
  

  define and understand the bayes theorem
  

  define a bayesian model in python
  

  explore the probability tables of nodes in a bayesian network
  

  predict values with bayesian models
  

  explore probabilities associated with a bayesian model
  

  create naive bayes models in python
  

  define descriptive and inferential statistics
  

  describe different types of probability distributions and where they occur
  

  analyze and visualize data using box plots
  

  recognize how data is distributed using histograms and violin plots
  

  calculate and visualize confidence intervals using python
  

  estimate a population's mean with confidence intervals
  

  describe binomial distributions and generate one using scipy
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  recount binomial distributions and generate one using scipy
  

  analyze a uniform distribution by using cumulative distribution and probability density functions
  

  apply poisson distributions to make estimates in real-life situations
  

  use poisson distributions to make estimates in real-life situations
  

  describe normal distributions and their characteristics
  

  explain the law of large numbers programmatically
  

  recall the symmetrical features of normal distributions
  

  describe the fundamentals of hypothesis testing
  

  set up null and alternative hypotheses for statistical tests
  

  interpret p-values using alpha levels
  

  compare and contrast type i and type ii errors in hypothesis testing
  

  explore one-sided and two-sided t-tests
  

  create a function to manually perform a t-test
  

  perform the wilcoxon signed-rank test to compare medians
  

  test medians using the wilcoxon signed-rank test
  

  perform t-tests on real-world data
  

  recall the assumptions of the two-sample t-test
  

  use the two-sample t-test to compare means
  

  use levene’s test to check for equal variances
  

  recognize when the welch’s t-test should be used
  

  describe type i and type ii errors
  

  perform the paired t-test on paired samples
  

  use the welch’s t-test to compare means
  

  recognize the use of the mann-whitney u-test
  

  use the mann-whitney u-test
  

  outline the use of one-way anova analysis
  

  use tukey’s hsd to know which categories differ significantly
  

  use the non-parametric kruskal-wallis test
  

  outline the use of the two-way anova analysis
  

  use two-way anova with interaction between the independent variables