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Mathematics for statistics Students

Probability of events

What are the various counting techniques

What is a sample space

What are the various properties of the probability measure

Conditional probability and Bayes theorem

How to evaluate conditional probabilities

How to use the Bayes' theorem

Random variables and distribution functions

What is the difference between discrete and random variable

How to use the distribution functions of discrete and random variables

How to determine the percentiles of a continuous random variable

Moments of random variables and Chebychev inequality

How to determine the moments of random variables

How to determine the expected value of a random variable

How to determine the variance of random variables

How to use the Chebychev inequality

How to use moment generating functions

Special discrete distributions

How to use the Bernoulli distribution

How to use the geometric distribution

How to use the Binomial distribution

How to use the negative binomial distribution

How to use the hypergeometric distribution

How to use the Poisson distribution

How to u the Riemann Zeta distribution

Special continuous distributions

How to use the uniform distribution

How to use the Gamma distribution

How to use the Beta distribution

How to use the normal distribution

How to use the lognormal distribution

How to use the Inverse Gaussian distribution

How to use the logistic distribution

Two random variables

How to differentiate bivariate discrete random variables and bivariate continuous random variables

How to use conditional distributions

How to determine the independence of random variables

Product moments of bivariate random variables

How to determine the Covariance of Bivariate Random variables

How to determine the independence of random variables

How to determine the variance of the linear combination of random variables

How to obtain the functional dependency of random variables using the correlation coefficients

Conditional expectation of bivariate random variables

How to determine the conditional expected values

How to determine the conditional variance

What is a regression function and how to graph it

Transformation of random variables and their distributions

How to use the distribution function method

How to use the transformation method for Univariate case

How to use the convolution method

How to use the transformation method for bivariate case

How to use the moment generating function method

Special discrete bivariate distributions

How to use the Bernoulli bivariate distribution

How to use the bivariate binomial distribution

How to use the Bivariate geometric distribution

How to use the bivariate negative binomial distribution

How to use the bivariate hypergeometric distribution

How to use the bivariate Poisson distribution

Special continuous bivariate distributions

How to use the bivariate uniform distribution

How to use the bivariate Cauchy distribution

How to use bivariate gamma distributions

How to use bivariate beta distributions

How to use the bivariate normal distribution

How to use bivariate Logistic distributions

Sequences of random variables and order statistics

How to determine sample mean and variance

What is the weak law of large numbers

How to use the Central limit theorem

How to determine order statistics

What is a sample percentile

Distributions associated with normal populations

What is a Chi-square distribution

How to use a student's t-distribution

How to use the Snedecor's F-distribution

Techniques for finding point estimators for parameters

How to use the maximum likelihood method

How to use the moment method

How to use the Bayesian method

Techniques for finding interval estimators for parameters

How to use the pivotal quantity method

How to construct a confidence interval for population mean

How to construct a confidence interval for population variance

How to construct an approximate confidence interval for parameter with MLE

How to use the statistical method

What are the criteria for evaluating confidence intervals

How to evaluate tests

Test of statistical hypotheses for parameters

How to find tests

Simple linear regression and correlation analysis

How to use the Least squares method

How to identify a normal regression analysis

Goodness of Fits tests

How to use the Kolmogorov-Smirnov test

How to use the Chi-square test