Week 4: Short cut to find expected value, variance, standard deviation, geometric model, binomial model

What happens to expected value and variance if you add a constant (C)?

E[X ± C] = E[X] ± C

• old E[X] ± constant

Var[X ± C] = Var[X]

• variance remains unchanged

What happens to expected value and variance if you add the possibilities of x to y?

E[X ± Y] = E[X] ± E[Y]

Var[X ± Y] = Var[X] + Var[Y]

• the variance of x is always added to the variance of y even if they’re subtracted!

• can only add the variance of x & y if independent!

What happens to expected value and variance if you multiply by a constant (a)?

E[aX] = aE[X]

Var[aX] = a² Var[X]

What are the 2 simple models?

1. Geometric

2. Binomial

What is a geometric model formula?

How many trials will it take until we get our first success?

p = probability of success

q = 1 - p (probability of failure)

x = # of trials until first success occurs

What is the expected value, variance, and standard deviation for geometric models?

What is the binomial model formula?

How many successes out of a number of trials?

x = # of successes

p = probability of success per trial

q = 1 - p (probability of failure)

n = number of trials

What is the expected value, variance, and standard deviation for binomial models?

What are factorials?

What is the coefficient for variation?