STUPIDSID
1 (a)
Explain concept of power spectral density.
5 M
1 (b)
State and prove Central Limit Theorem.
5 M
1 (c)
Explain properties of cross correlation function.
5 M
1 (d)
State and prove Baye's theorem.
5 M
2 (a)
Box 1 contains 5 white balls and 6 black balls. Box 2 contains 6 white & 4 black balls. A box is selected at random and then a ball is chosen at random from the selected Box
i) What is the probability that the ball chosen will be a white ball
ii) Given that the ball chosen is white what is the probability that came from box1.
i) What is the probability that the ball chosen will be a white ball
ii) Given that the ball chosen is white what is the probability that came from box1.
10 M
2 (b)
Give the properties of CDF, PDF and PMF.
10 M
3 (a)
Explain concept of conditional probability and properties of conditional probability.
10 M
3 (b)
Explain what do you mean by?
i) Deterministic system
ii) Stochastic system
iii) Memoryless system
i) Deterministic system
ii) Stochastic system
iii) Memoryless system
3 M
3 (c)
Prove that if input to memoryless system is strict sense stationary (SSS) process then output is also strict sense stationary.
7 M
4 (a)
Explain Random process, define ensemble mean, Auto correlation and Auto covariance of the process in terms of indexed random variables in usual mathematical forms.
10 M
4 (b)
Let Z=X+Y. Determine pdf of Z fz (Z).
10 M
5 (a)
State and prove Chapman Kolmogorov equation.
10 M
5 (b)
Explain Chebyshev's Inequality with suitable example.
10 M
6 (a)
The joint probability density function of two random variables is given by \[ F_{xy}(x, y)=15 \ e^{-3x-3y}; \ \ x\ge 0, y\ge 0 \] 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 Independent?
iv) Find E(x/y) and E(y/x).
ii) Find the marginal densities of X and Y
iii) Are X and Y Independent?
iv) Find E(x/y) and E(y/x).
10 M
6 (b)
Write short notes on following special distributions
i) Poisson distributions
ii) Rayleigh distributions
iii) Gaussian distributions
i) Poisson distributions
ii) Rayleigh distributions
iii) Gaussian distributions
10 M
More question papers from Random Signal Analysis