Question

If U(t) = X cos t + Y sin t and V(t) = Y cos t + X sin t, where X and Y are independent RV’s such that E(X) = 0 = E(Y), E(X^2) = E(Y^2) = 1, show that {U(t)} and {V(t)} are individually stationary in the wide sense, but they are not jointly wide-sense stationary.

Name: if ut x cos t y sin t and vt y cos t x sin t where x and y are independent rvs such that ex 0 ey ex2 ey2 1 show that ut and vt are individually stationary in the wide sense but they are not 37643
Uploaded: 2021-12-10T09:50:30-08:00
Duration: 6 min 25 s
Channel: Croup Chais
Description: if ut x cos t y sin t and vt y cos t x sin t where x and y are independent rvs such that ex 0 ey ex2 ey2 1 show that ut and vt are individually stationary in the wide sense but they are not 37643

          If U(t) = X cos t + Y sin t and V(t) = Y cos t + X sin t, where X and Y are independent RV’s such that E(X) = 0 = E(Y), E(X^2) = E(Y^2) = 1, show that {U(t)} and {V(t)} are individually stationary in the wide sense, but they are not jointly wide-sense stationary.

Added by Megan H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Croup Chais

12/10/2021

Step 1

We have: E[U(t)] = E[X cos t + Y sin t] = E[X] cos t + E[Y] sin t = 0 E[V(t)] = E[Y cos t + X sin t] = E[Y] cos t + E[X] sin t = 0 Show more…

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If U(t) = X cos t + Y sin t and V(t) = Y cos t + X sin t, where X and Y are independent RV’s such that E(X) = 0 = E(Y), E(X^2) = E(Y^2) = 1, show that {U(t)} and {V(t)} are individually stationary in the wide sense, but they are not jointly wide-sense stationary.