STUPIDSID
1 (a)
Discuss the properties of cross correlation function
5 M
1 (b)
If A and B are two independent events then prove that P(A∩B)= P(A) P(B )
5 M
1 (c)
State and explain Bayes Theorem
5 M
1 (d)
Suppose five cards to be drawn at random form a standard deck od cards. If all the drwan cards are red what is the probability that all of them are hearts?
5 M
2 (a)
A random variable has the following exponential probability density function : f(x)=Ke-|x|. Determine the value of K and corresponding distribution function
10 M
2 (b)
Define discrete and continuous random variables by giving examples. Discuss the properties of distribution function.
10 M
3
The joint probability density function of two random variables is given by
fx,y(x,y)=15e-3x-3y : x≥0, y≥0
(i) Find the probability that x<2 and y>0.2
(ii) Find the marginal densities of x and y
(iii) Are x and y independant.
(iv) Find E(x/y) and E(y/x)
fx,y(x,y)=15e-3x-3y : x≥0, y≥0
(i) Find the probability that x<2 and y>0.2
(ii) Find the marginal densities of x and y
(iii) Are x and y independant.
(iv) Find E(x/y) and E(y/x)
20 M
4 (a)
State and prove the Chapman-Kolmogorov equation.
10 M
4 (b)
Write short notes on the following special distributions
(i) Poisson distribution (ii) Reyleigh distribution and (iii) Gaussian distribution
(i) Poisson distribution (ii) Reyleigh distribution and (iii) Gaussian distribution
10 M
5
(a) Suppose X and Y are two random variables. Define covariance and correlation of X and Y. when do we say that X and Y are
(i) Orthogonal
(ii) Independent and
(iii) Uncorrelated> Are uncorrelated variables independent?
(b) What is random process? State four classes of random process giving one example of each.
(i) Orthogonal
(ii) Independent and
(iii) Uncorrelated> Are uncorrelated variables independent?
(b) What is random process? State four classes of random process giving one example of each.
10 M
6 (a)
Explain power spectral density function. State its important properties and prove anyone of the property.
10 M
6 (b)
Prove that if input to LTI system is w.s.s. then the output is also w.s.s.
10 M
7 (a)
Define Central Limit Theorem and give its significance
5 M
7 (b)
Describe sequence of ramdom variables
5 M
7 (c)
A stationary process is givien by X(f)=100 cos[100 t+θ] where θ is a random variable with uniform probability distribution in the interval [-π, π]. Show that it is a wide sense stationary process.
10 M
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