Question: For random variables, if their covariance is equal to zero, then they are uncorrelated. For random variables, their inner product is denoted by <

For random variables, if their covariance is equal to zero, then they

For random variables, if their covariance is equal to zero, then they are uncorrelated. For random variables, their inner product is denoted by < X,Y >= E(XY), if E(XY) = 0, they are called orthogonal, and denoted by 1 1. Suppose we have a random variable X with a uniform distribution X~ unif(-1,2), and Y = h(X) = kX2, where is (k = 0) is constant. Is X and Y correlated? independent? orthogonal? 2. Suppose we have a random variable X with a uniform distribution X~ unif(-1,2), and Y = h(X) = kX2 +c, where is (k = 0, c0) are both constants. Is X and Y correlated? independent? orthogonal? 3. Suppose we have a random variable X with a uniform distribution X~ unif(-1, 1), and Y = h(X) = kX2, where is (k = 0) is constant. Is X and Y correlated? independent? orthogonal? 4. If X and Y are uncorrelated, will X,Y be orthogonal? What is your conclusion about correlation and orthogonality?

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Solutions i assumed orthogonal is denoted by L To determine whether X and Y are correlated independent or orthogonal we need to calculate their covariance and check if it is equal to zero Covariance C... View full answer

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