Properties of expectation  Discrete Probabilities
Properties of expectation
Basic concepts:
 Center of a data set: mean, median, mode
Lessons
Notes:
We can write out mean as an expected value:
$\mu=E[X]$
And likewise for variance:
$\sigma^2=$ Var$(X)$
n: number of trials
x: number of success in n trials
p: probability of success in each trial
Binomial:
$E[X]=np$
Var$(X)=np(1p)$
Geometric:
$E[X]=\frac{1}{p}$
Var$(X)=\frac{1p}{p^2}$
Properties of Expectation:
$\cdot$ $E[X+a]=E[X]+a$
$\cdot$ $E[bX]=bE[X]$
$\cdot$ $E[X+Y]=E[X]+E[Y]$
Or in full generality:
$\cdot$ $E[X_1+X_2+ \cdots +X_n ]=E[X_1 ]+E[X_2 ]+ \cdots +E[X_n]$
Properties of Variance:
$\cdot$ Var$[X+a]=$ Var$[X]$
$\cdot$ Var$[bX]=b^2$Var$[X]$
$\cdot$ Var$[X+Y]=$ Var$[X]+$ Var$[Y]$ if X and Y are independent

1.

3.
A certain car breaks down every 50 hours of driving time. If the car is driven for a total of 175 hours;

4.
Clara is trying to make the perfect teapot out of pottery. Each time she attempts to make the perfect teapot she will use a lump of clay and she will succeed with a probability of 0.20. Once she makes the perfect teapot she will stop potting.

6.
Suppose we have two independent random variable one with parameters $E[X]=4$ and Var$(X)=3$, and the other with parameters $E[Y]=9$ and Var$(Y)=6$.