{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 5b

# Chapter 5b - CH 5 Part 2 Functions of Random...

This preview shows pages 1–6. Sign up to view the full content.

CH 5 Part 2 – Functions of Random Variables (Really Sec. 4.8, 5.5) 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Functions of Random Variables Rules Regarding Expectation/Variance: Let Y = X + c, where X is a random variables with mean μ and variance σ 2 and c is a constant. E(Y) = E(X + c) = E(X) + E(c) = E(X) + c = μ + c Var(Y) = Var(X + c) = Var(X) + Var(c) = Var(X) = σ 2 Let Y=cX. E(Y) = E(cX) = c*E(x) = c μ Var(Y) = Var(cX) = c 2 Var(X) = c 2 σ 2
How do we find the distribution function for this new variable? Univariate (one variable) case: (Sec. 4.8) Suppose we have one continuous random variable X, and define Y = g(X), where g is strictly monotonic and differentiable. Then f(y) = where g -1 (y) is the function of g(x) solved for x, and d g -1 (y)/dy is the derivative of g(x) w.r.t. y. | ) ( | ))* ( ( 1 1 dy y dg y g f x - - 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Univariate Example Let f(x) = 2X, 0 < X < 1. We have found that E(X) = 2/3 and Var(X) = 1/18 . We create Y=g(X)=3X+6. (a)Find the probability distribution for Y. 4
5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 17

Chapter 5b - CH 5 Part 2 Functions of Random...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online