3) Expectation Flashcards
What is the expectation of a discrete random variable
What is the expectation of a continuous random variable
What is the variance of a random variable X
What is the expectation of a function g(X) for discrete and continuous
What is the expectation of a function g(X,Y) for discrete and continuous
How can the expectation E[g(X,Y)] be expressed when g is just a function of x
What is the linearity of expectation for two functions 𝑔1 and g2 and real numbers α and β
What is the expectation of the product of two functions g(X) and h(Y) for independent random variables X and Y
What is the variance of the linear combination αX+βY for independent random variables X and Y
What is the covariance between random variables X and Y
What are the properties of covariance
What is the variance of the linear combination αX+βY for dependent random variables X and Y
What is the variance of the linear combination ∑aiXi for dependent random variables X1 ,…,X and constants a1,…,an
What is the variance of the linear combination ∑aiXi for independent random variables X1 ,…,X and constants a1,…,an
What is the Cauchy-Schwarz inequality
What is the correlation coefficient
When are two random variables uncorrelated
If Cov(X, Y ) = 0
(Independent random variables are uncorrelated)
What is the the conditional expectation of X given Y = y, for discrete random variable (X, Y )
What is the the conditional expectation of X given Y = y, for continuous random variable (X, Y )
What is the the conditional expectation of g(X, Y ) given Y = y
What is the Law of total expectation
How is the law of total expectation expressed for continuous and discrete random variables
What is the conditional expectation of[α(X)g1(X, Y ) + β(X)g2(X, Y ) given X
What is the conditional expectation E[g(X)∣Y] when X and Y are independent
What is the conditional variance of Y given X = x
What is the law of total variance
