Chapter 4 - Continuous Random Variables Possible values are...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Continuous Random Variables Possible values are any value in some interval of the real number line. The number of possible values is uncountably infinite Density function f(x) is the probability density function (PDF) probability = area under a curve ( ) ( ) b a P a x b f x dx = has two properties: 1) f(x) > 0 (non-decreasing function) 2) (integrating over region for which x is defined results in 1) If X is continuous, then P(x 1 < X < x 2 ) = P(x 1 < X < x 2 ). The result is the same whether we use greater than or greater than/equal to. WHY? Cumulative Distribution Function For a continuous random variable, X, the CDF ( ) ( ) ( ) x F X P X x f t dt- = = Note: f(x) is the derivative of F(x) w.r.t. x. - = 1 ) ( dx x f Expected value ( ) For a continuous variable x, the expected value is = ( ) * ( ) X E x x f x d x = Variance ( 2 29 2 = 2 2 ( ) [ ] ( [ ]) Var x E x E x =- where 2 2 [ ] * ( ) X E x x f x d x = Examples: (1) Let f(x) = 1.5x 2 for 1 < x < 1....
View Full Document

Page1 / 13

Chapter 4 - Continuous Random Variables Possible values are...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online