{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

handout_week3_a

# handout_week3_a - Stochastic Signals and Systems Random...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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.

Unformatted text preview: Stochastic Signals and Systems Random Variables Virginia Tech Fall 2008 Uniform Random Variable The pdf of the uniform random variable is given by: f X ( x ) = 1 b- a a ≤ x ≤ b x < a and x > b And the cdf is given by: F X ( x ) = x < a x- a b- a a ≤ x ≤ b 1 x > b Gaussian (Normal) Random Variable The pdf for the Gaussian random variable is given by f X ( x ) = 1 √ 2 πσ exp- ( x- m ) 2 2 σ 2 ! where m and σ are the mean and standard deviation, respectively. The Gaussian pdf is a “bell-shaped” curve centered and symmetric about m and whose “width” increases with σ . Gaussian (Normal) Random Variable The cdf for the Gaussian random variable is given by Definition: Q ( ξ ) = 1 √ 2 π Z ∞ ξ e- t 2 / 2 dt (Q-function) erfc ( ξ ) = 2 √ π Z ∞ ξ e- t 2 dt (Complementary error function) erf ( ξ ) = 1- erfc ( ξ ) (Error function) Exponential Random Variable The exponential random variable X with parameter λ has pdf f X ( x ) = x < λ e- λ x x ≥ and cdf F X ( x ) = x < 1- e- λ x x ≥ • The exponential random variable arises in the modeling of the time between occurrence of events (e.g., the time between customer demands for call connections)....
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

handout_week3_a - Stochastic Signals and Systems Random...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online