1. ## Random Variables

How do I solve this question?

Q: Let X be a random variable with mean x and standard deviation y. consider a new random variable Z, obtained by subtracting x from X and then dividing the result by y. Use the laws of expected value and variance to prove:
a) That the expected value of Z= 0
b) That both the variance and standard deviation of Z are equal to 1.

2. Originally Posted by muffin628
How do I solve this question?

Q: Let X be a random variable with mean x and standard deviation y. consider a new random variable Z, obtained by subtracting x from X and then dividing the result by y. Use the laws of expected value and variance to prove:
a) That the expected value of Z= 0
b) That both the variance and standard deviation of Z are equal to 1.

What "laws of expected value and variance" have you been taught. Please list them and then state what your difficulty is in using them.

3. law of expected value:
c is a constant. X is a random variable.

1) E(c)= c
2) E(X+c)= E(X)+c
3) E(cX)= cE(X)

laws of variance:
1) V(c) = 0
2) V(X+c) = V(X)
3) V(cX) = c^2 x V(X)

4. $\displaystyle E\left( {\frac{{X - x}} {y}} \right) = E\left( {\frac{X} {y} - \frac{x} {y}} \right) = \frac{1} {y}E\left( X \right) - \frac{x} {y} = ?$

5. Originally Posted by muffin628
law of expected value:
c is a constant. X is a random variable.

1) E(c)= c
2) E(X+c)= E(X)+c
3) E(cX)= cE(X)

laws of variance:
1) V(c) = 0
2) V(X+c) = V(X)
3) V(cX) = c^2 x V(X)
$\displaystyle Var(aX + b) = a^2 Var(X)$. In your problem, what is a and what is b ....?