Question3 (a) The discrete process x[n] is wide sense stationary (WSS) with Rx[m

Question

Question3 (a) The discrete process x[n] is wide sense stationary (WSS) with Rx[m] 36fm]. It is applied to a linear-shift invariant system with the following input-output relationship: (i) Find the impulse response of the system h[n]. [7 marks] (ii) Find Efy' [n]) [6 marks] (b) In a group of 55 students: Find the probability that at least two students have the same birthday. If necessary, use the approximation e* 1+x when x is small [6 marks] (ii) Find the probability that at least one student has birthday on January 1st. [6 marks]

Explanation / Answer

Solving part B

I> Group of 55 Students

At least 2 student have birtday on the same day = 1- (364/365)^55C2= 0.9829909

II> Probability that 1 student has Birtday on 1st Jan

Probability of 1st Jan can selected from 365 days= 1/365

Out of 55 Students at least 1 student has birth day = (55C1)= 55!/!!

So Probability of at least 1 student has birtda of 1st Jan= 55C1* 1/365= .15068493

A> Unable to solve part A.

End of Answer!!

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