Sentence examples for be two independent random from inspiring English sources

Let X, Y be two independent random variables with associated probability measures (mu,nu) respectively.

Let X, Y be two independent random variables with known distribution having the probability density function (phi_{1}(x)) and (phi_{2} y)), respectively.

Let X, Y be two independent random variables and (Z=f X,Y)) be a function of the random variables X and Y. Then Ebigl sigma^{2}(Z|X bigr)leqsigma^{2} bigl(E Z|Y bigr).

(19) On the other hand, let V and T be two independent random variables such that V is uniformly distributed on ([0,1]) and T has the exponential density (rho _{1} (theta )) defined in (19).

Let and be two independent random sequences and let us further assume that there are no sequencing errors.

Cochran's theorem [21] states that the sample mean and variance are two independent random variables.

Therefore, if where and are two independent random signals, we have: (19).

Therefore, if where and are two independent random signals, we have: (21) and, after Fourier transform, we obtain: (22)  .

hbox {End for} end{array}nonumber end{aligned} (4 where (r_1) and (r_2) are two independent random sequences, (r_1sim U(0,1)) and (r_2 sim U 0,1)).

As described in the proof of Theorem 5, x ̂ 1 and x ̂ 2 are two independent random variables that follow exponential and Chi-squared distributions, respectively.

Therefore, if where and are two independent random signals, we have: (19) and, after Fourier transform, we obtain: (20)   (ii) The moment of the product is equal to the product of the moments if the signals are independent.