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1) A random variable has an exponential PDF given by f(x)=ae-bIxI

Where, a and b are constant. Determine:

a) Relationship between a and b.

b) The distribution function of x.

2) Determine the mean, variance and standard deviation of random variable of x that is uniformly distributed between 0 and 10.

3) Consider the two process x(t) and y(t) be described as:

x(t)=A cos wt +Bsinwt

y(t)=Bcos wt-A sinwt,

Where, A and B are random variable and w is a constant.

If A and B are uncorrelated random variable with zero and equal variance. Prove that x(t) and y(t) are jointly WSS.

4) Prove that random process x(t)= Acos (wt +θ) is WSS where A,w are constants and θ is uniformly distributed within the interval (0,2Π).

5) Describe the properties of the mutual information.

6) prepare a brief notes on the Binary Symmetric Channel.

7) Consider the message S={S1,S2,S3,S4,S5,S6,S7,S8}

P={1/4,1/4,1/8,1/8,1/16.1/16,1/16,1/16} X={0,1}

Using the Shannon fano coding.

8)  Apply the Huffman coding procedure for S={S1,S2,S3,S4,S5,S6,S7}

P={0.4,0.2,0.12,0.08,0.08,0.08,0.04} X={0,1}

9) Deduce the expression for noise figure form the cascaded stages or the friss formula.

10) describe the concept of the Neyman Pearson test.

Electrical & Electronics, Engineering

• Category:- Electrical & Electronics
• Reference No.:- M912734

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