Description
1 Definitions
1) The Z transform of X is defined as
MX(z) = E z−kpX(k) (1.1)
2) Let X be a random variable with pmf.
pX(k) = 10/6 1 ≤ k ≤ 6
otherwise
X is said to be Discrete Uniform Random Variable
3) Convolution of two sequences using Toeplitz matrices (1.2)
y=x⊛h (1.3)
h231 h12 .3 . . 0 h 0 . . . 0
x1
x2
h h h . . 0
.
y= hm−1 . . . h2 h1 . (1.4) hm hm−1 . . . h2 .
. . . . . . . 0 0 . . . hm
. . . . . .
xn
2 Problems
1. If xy.
2. Find pX1(k)⊛ pX2(k) using toeplitz matrices.
3. Find MY(z), such that Y = X1 +X2
4. Find pY(k)
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