Random variables

Concepts

• Random variable 10 exercisesA random variable X is a function that assigns a real number to each outcome of the sample space Omega of a random experiment.
• Probability mass function 10 exercisesThe probability mass function p_X of a discrete random variable X gives, for each value x it can take, the probability P that it…
• Probability density function 10 exercisesThe density function f of a continuous random variable X is a nonnegative function such that the area under its graph over an int…
• Cumulative distribution function 10 exercisesThe cumulative distribution function F_X of a random variable X gives, for each real number x, the probability P that X takes a v…
• Expected value 10 exercisesThe expectation E[X] of a random variable X is the average of its possible values, each weighted by its probability.
• Variance 10 exercisesThe variance Var(X) of a random variable X measures how spread out its values are around its expectation E: it is the expected va…
• Covariance 10 exercisesThe covariance Cov(X,Y) of two variables X and Y measures whether they tend to deviate from their expectations E in the same or o…