Suppose three random variables X , Y , Z have a joint distribution.
PU,PV,W(u,v,w)=toproaba gooas.P(not mov eveuy now)
Then, U and V are independent when in respect to Z at the exit was printron.
False
To determine whether U and V are independent with respect to Z, we need to examine the joint distribution of U, V, and Z.
Given the joint distribution PU,PV,W(u,v,w), the independence condition states that the joint distribution can be factored into the product of the marginal distributions:
PU,PV,W(u,v,w) = PU(u) × PV(v) × PZ(w)
In other words, if U and V are independent, the probability of U and V taking certain values should not depend on the value of Z.
From the given statement "PU,PV,W(u,v,w)=toproaba gooas.P(not mov eveuy now)", it is not clear whether the joint distribution can be factored into the product of the marginals. Therefore, we cannot conclude that U and V are independent with respect to Z based on the given information.
In summary, the statement "U and V are independent with respect to Z" is false based on the given information.