Chapter 4 - Random Variables Flashcards
Define a random variable.
State Lemma 4.2 on Borel sets and r.v’s.
Define the distribution function of a random variable.
Define the probability mass function of a discrete random variable.
State the mass function of the poisson and binomial distributions.
Define a continous random variable, and hence the density function.
State Lemma 4.8 creating eight new random variables from existing ones.
State Lemma 4.9 on random variables and Borel functions.
Define a simple function and the integral of a simple function.
Define the integral of a positive function.
Define an integrable function.
Define expectation.
State Lemma 4.12 on integrating over Borel functions of continuous random variables.
What is the expectation of X for continuous random variables?
State the nine basic properties of expectation, including the MCT and BCT.
State Markov’s Inequality.
Define variance and standard deviation.
State Chebychev’s Inequality.
Define independent random variables.
State Proposition 4.19 on Borel functions and independent variables.
State Proposition 4.20 on expectations of products of random variables.
State Lemma 4.21 on variance of sums of random variables.
