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

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

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

Summary A Confidence Interval is an interval of numbers containing the most plausible values for our Population Parameter. A confidence level can be any value between, and not including, 0% and 100%. The higher the value, the larger the confidence level and the more the confidence interval will include the actual population mean. An increase … Read more

Summary A box and whiskers diagram displays a summary of a set of data. Maximum, Minimum, First Quartile, Third Quartile and Median, interquartile, upper limit, lower limit. Outlier can be present in the measurement, they thus need to be shown separately on the box and whiskers diagram. A box and whiskers diagram A box and … Read more