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) Write 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) Explain the concept of the Neyman Pearson test.