Ch1 - Discrete Random Variables

What is a random variable?

A variable whose value depends on a random event

What is the expected value of a random variable X denoted as?

$$E\left(X\right)$$

How do you find the expected value of a random variable X?

$$E\left(X\right)=\sum xP(X=x)$$

What does the sum of probabilities equal?

$$\sum P(X=x)=1$$

What does $P\left(X^2=4\right)$ = ?

$$P\left(X^2=4\right)=P\left(X=2\right)+P\left(X=-2\right)$$

How is variance of X usually written?

$Var\left(X\right)$, or $\sigma$

How is the variance of X usually found?

$$Var\left(X\right)=E\left(X^2\right)-\left(E\left(X\right)\right)^2$$

If X and Y are random variables, then what does $E(X+Y)$ = ?

$$E(X+Y)=E(X)+E(Y)$$

If X is a random variable and a and b are constants, what does $E(aX+b) =?$

$$E(aX+b)=aE(X)+b$$

If b is a constant, what is $E(b)$ = ?

$$E(b)=b$$

If X is a random variable and a and b are constants, what does $Var(aX+b)$ = ?

$$Var(aX+b)=a²Var(X)$$