3.2: Conditional Expectations and Expected Value Flashcards
The Expected Value of a random variable is..
Expected Value is denoted as..
The probability-weighted average of the possible outcomes of the random value.
E(x)
Formula for Expected Value of multiple variables:
E(X) = P(X1)X1 + P(X2)X2 + … P(Xn)Xn = ∑ni P(Xi)Xi (summation)
Where Xi is one of n possible outcomes of the random variable X.
The Variance of a Random Variable is…
The expected value (probability-weighted average) of squared deviations from the random variable’s expected value.
The Variance of a Random Variable formula (sample):
Sigma^2(X) = E {[X – E(x)]^2}
What does the Variance of a Random Variable indicate if more than 0?
Dispersion of outcomes.
Standard Deviation is a measure of dispersion that is..
It is the positive square root of?
In the same units as the data.
It is the positive square root of Variance.
Standard Deviation formula (both):
Stand.Dev = Root of Σ(X - x̄)^2 / N POPULATION
Stand.Dev = Root of Σ(X - x̄)^2 / N - 1 SAMPLE
Conditional Expected Value is the expected value of..?
A stated event given that another event has occurred.
Conditional Expected Value is calculated as?
E(X | S) = P(X1 | S)X1 + P(X2 | S)X2 + … + P(Xn | S)*Xn
Total Probability Rule for Expected Value is a rule explaining…
The expected value of a random variable in terms of expected values of the random variable conditional on mutually exclusive and exhaustive scenario.
Total Probability Rule for Expected Value formula’s for 2 scenarios..
For 2 scenarios: E(X) = E(X | S)P(S) + E(X | Sc)P(Sc)
Once we know expected returns on individual securities…
We immediately have the expected return on the portfolio Rp.
Expected Portfolio Return formula is:
E (Rp) = w1E(R1) + w2E(R2) + w3E(R3)… + wnE(Rn)
Covariance measures the direction of…
The relationship between two variables
Covariance of two variables in a sample is calculated as?
COV(X,Y) = Σ(Xi - x̄)*(Yi - ȳ) / N - 1
