Probability Theory and Stochastic Processes Mid - II, November - 2014

1.Two independent random variables x, y are always
  • Correlated
  • Uncorrelated
  • have Cov (x, y) = 0
  • have correlation coefficient -1
Answer: B
2.Which of the following is correct?
  •  > 1
  • -  <  < 
  • 0 <  < 
  • -1 <  < 1
Answer: D
3.The mean square value for the poission process x(t) with parameter t is
  • t
  • (t)2
  • t + (t)2
  • t - (t)2
Answer: C
4.The cross spectral density Syx (ω) =
  • SXY(ω)
  • SXY(-ω)
  • Syx(-ω)
  • - Syx(ω)
Answer: B
5.Let Sxy (ω) = 0 and Syx (ω) = 0 if X(t) and Y(t) are
  • Orthogonal
  • not orthogonal
  • constant
  • none of the above
Answer: A
6.The autocorrelation function of stationary random process x(t) is .The mean and variance is
  • 4, 25
  • 21, 2
  • 5, 4
  • 25, 4
Answer: A
7.If the future value of a sample function cannot be predicted based on its past values , the process is referred to as
  • Deterministic process
  • Non - Deterministic process
  • Independent process
  • Statistical process
Answer: B
8.If x and y are two independent random variables , then ะคX+Y(ω) is
  • Φxy(ω)
  • Φx(ω)Φy(ω)
  • Φx(ω)+Φy(ω)
  • Φyx(ω)
Answer: B
9.If x and y are independent, then p is
  • 1
  • 0
  • -1
  • none of the above
Answer: B
10.Joint density function of two random variables is given by for 2 < x <  and [ ] 0 < y < 1 then E[x] is
  • 6
  • 9
  • 3
  • 1
Answer: C
11.If the random variables X and Y are orthogonal , then their correlation function is ______
Answer: zero
12.Gaussian random variables are completely defined through only their ___________
Answer: First order and second, order moments
13.The time average of the product x(t) and x(t+τ) is called ____________of x(t)
Answer: auto correlation function
14.If x(t) is periodic , then its autocorrelation function is _________
Answer: periodic
15.The average power of Pxy is _______
Answer: Pyx
16.The power density spectrum and the _________of the auto correlation function from a Fourier transform pair.
Answer: time average
17.IM[Sxy(w)] is an _____function.
Answer: odd
18.The autocorrelation function of a WSS random process is used to study _________haracteristics.
Answer: spectral
19.A random process is a function of ____________
Answer: sample space and time
20.The expected value of a time function is called the _________ of that function.
Answer: time average