1. Are the following statements correct? A simple YES or NO will do, but read th
ID: 3322404 • Letter: 1
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1. Are the following statements correct? A simple YES or NO will do, but read the statements carefully (b) If X and Y are random variables that have an exponential distribution, then their sum X+Y also has an exponential distribution (c) If (X, Y) is a jointly Gaussian random vector, then X and Y are independent if and only if they are uncorrelated. (a) If (x,y) is a jointly Gaussian random vector, then the best linearstiate E(xV) forX in terms of Y is also the best overall (i.e., least squares) estimate for X in terms of Y (e) According to the central limit theorem, any large number of identically distributed random variables is approximately Gaussian. (f) The Wiener process has stationary and independent increments (g) The covariance function of a stochastic process is positive definite. (h) White noise is a Gaussian stochastic process (i) A zero mean Gaussian stochastic process is stationary if and only its covariance function R(s,t) is only a function of the difference of times, i.e., R(s, t) R(t s). G) Two wide sense stationary processes which have the same mean and covariance are equalExplanation / Answer
a) yes , every subset of R is a borel set
b) no , sum for two exponential r.v's is not an exponential variable.
c) yes. Two variables are uncorrelated.
e) yes
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