KERALA UNIVERSITY Class 4 probability random processes and numerical techniques Question Paper 2019

Practice authentic previous year questions for better exam preparation.

Sample Questions

If $f(x)=\frac{k}{2^{x}}$ is a probability distribution of a random variable which can take values $x=0,1,2,3,4$. Find $K$ and Mean of the distribution.
(a) A Random variable has the following probability distribution | $X$ | -2 | -1 | 0 | 1 | 2 | 3 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | $f(x)$ | $1 / 10$ | $k$ | $1 / 5$ | $2 k$ | $3 / 10$ | $3 k$. | Find :
(b) If $f(x, y)=2$ for $0<x<1,0<y<x$ is the joint probability density function of random variables $X$ and $Y$, find the marginal and conditional density functions. Are $X$ and $Y$ are independent?
(a) If the auto correlation function of a random process is $R(\tau)=\rho e^{-\rho|\tau|}, \rho>0$, show that the spectral density is given by $S(w)=\frac{2}{1+\left(\frac{w}{\rho}\right)^{2}}$.
(a) If the auto correlation function of a WSS process is $R(\tau)=\rho e^{-\rho|\tau|}, \rho>0$, show that $X(t)$ is mean ergodic.