Consider RVX with cdf Fx 14 x 1 1 ux1 ux4 ux 4 Graph Fx Fi

Consider RVX with cdf F(x) = 1/4 [(x- 1) +1] [u(x-1)- u(x-4)] + u(x -4) Graph F(x) Find the pdf fx(x) Find P(X > 1) A transmitter sends a signal voltage X = +2 with probability 0.4 and a signal voltage X = - 2 with probability 0.6. The signal is corrupted by a noise N given by a Gaussian rv with mean 3 and s.d.2. Find the pdf of the received signal Y=X+N.

Solution

note: u have asked 2 question in one, we are suppose to answer 1 question at a time. so i will give you answer of question 2.

X = 2 PROBABILITY = 0.4 AND X = -2 WITH PROBABILITY 0.6.

N is with mean 3 and s.d = 2

Y = X + N

N = 3+2 = 5

3-2 = 1

MEAN = 3

Y = X+N

PDF = WHEN X= +2 , THEN PROBABILITY Y = X+N = 0.4

WHEN X=-2, THENPROBABILITY Y = X+N = 0.6