Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from to 1.

The voltage is processed by a “hard limiter”

with cutoff values and .5, so the limiter output is a random variable Y related to X by if if

, and if .

a. What is ?

b. Obtain the cumulative distribution function of Y and graph it.

P(Y 5 .5)

X . .5 Y 5 2.5 X , 2.5 Y 5 X |X| # .5, Y 5 .5 2.5 21 E(Xn

)

sX X 5 sX P(.25 # X # .5)

P(.25 , X # .5)

P(X # .5)

f(x) 5 e 90x8

(1 2 x) 0 , x , 1 0 otherwise ft3 f(x) 5 •

k x4 x . 1 0 x # 1