# Question: Suppose HX z is the probability generating function of some

Suppose HX( z) is the probability- generating function of some random variable X with PMF PX( k) . In terms of PX( k) , find the PMF of the random variable Y if its probability- generating function is given as in each of the following cases.

(a) HY (z) = HX (z / 2)

(b) HY (z) = HX 2 = ( z) .

(c) HY (z) = zmHX( z) .

(d) HY (z) = HX( z– 1).

(a) HY (z) = HX (z / 2)

(b) HY (z) = HX 2 = ( z) .

(c) HY (z) = zmHX( z) .

(d) HY (z) = HX( z– 1).

## Answer to relevant Questions

Derive an expression for the moment- generating function of a Rayleigh random variable whose PDF is The current flowing through a 75 Ω resistor is modeled as a Gaussian random variable with parameters, m = 0A and σ = 15 mA . Find the average value of the power consumed in the resistor. Let X be an Erlang random variable with PDF, Derive a saddle point approximation for the left tail probability, Pr (X< xo). Compare your result with the exact value for 0 ≤ xo < E [X]. Following the lead design an optimum 2- bit quantizer for a signal whose samples follow a triangular PDF, (a) Find the four quantization levels, { y1 ,y2 ,y3 ,y4}, and the three boundary points, { x1, x2, x3}. (b) Find the ...In Exercise 4.90 let the transmission time be Tt seconds for a packet. If the packet was received incorrectly, then a message is sent back to the transmitter that states that the message was received incorrectly. Let the ...Post your question