Hypothesis Testing

Summary Hypothesis testing is just a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. The “Null Hypothesis” denoted as , this means testing a claim that already has some established parameters. The “Alternative Hypothesis” is denoted as , this is known as the research … Read more

Histograms & Cumulative Frequency

Summary A histogram show the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable For a histogram In order to calculate the frequency density, we use Cumulative frequency is accumulation of the frequencies First plot the graph and then join up the points to make a cumulative curve … Read more

Expectation and Variance

Summary Expected value of a random variable Expected value of f(X) is defined by Var(X) is defined by Standard deviation is the under root of variance Expected value When we describe probability, we think of taking chances e.g if I bought a lottery ticket, what are the chances that I am going to win the … Read more


Summary Estimator is a statistic intended to approximate a parameter governing the distribution of the data. Estimator is denoted by a hat i.e    denotes an estimator of  . Sample Mean :  Sample variance: An estimator is said to be consistent if the variance of the estimator tends to zero as  An absolute efficiency of … Read more

Discrete Random Variables

Summary If X is a discrete random variable, the function given by f (x) = P(X = x) The sum of all the probability will always equal to one. The cumulative distribution function, F(x) for a random variable X is defined as the probability of certain events that exist. Cumulative probabilities provide, for each value … Read more

Continuous Random Variable

Summary If [a, b] are the domain of the continuous random variable function f and f(x) > 0 then:  Cumulative probabilities provided, can be represented as: Differentiating cdf always gives you probability density function. to find the probability of X that is in an interval P(a ≤  X  ≤ b) = P(X  ≤  b) – … Read more