Hi All,I have very simple question. Suppose we have two series of numbers, say A and B. A has 60% positive numbers and B have 40% positive numbers. I define a product of A and B as C=A*B. Could you please tell me how many positive numbers are positive in C? To make it clear 40*60+(1-40)*(1-60) is not the correct answer. Please help me with correct answer.RegardsGaurav

QuoteOriginally posted by: gauravkumar2Hi All,I have very simple question. Suppose we have two series of numbers, say A and B. A has 60% positive numbers and B have 40% positive numbers. I define a product of A and B as C=A*B. Could you please tell me how many positive numbers are positive in C? To make it clear 40*60+(1-40)*(1-60) is not the correct answer. Please help me with correct answer.RegardsGauravThis is not accurate solution. It is just a hint. Let us choose arbitrary from A and B sets of 10 numbers. First contains 6 jointly independent uniformly distributed ' +1' and other 4 are '-1'. B has inverse: 4 uniformly independently distributed ?+1' and other '-1'. Calculate expectation of the '+1' in pointwise product. It looks the answer. Probably more accurate it would be if we use special talk using the words ' in average'. In this case, we will deal with expected values from very beginning.

Assuming "we will deal with expected values from very beginning" (i.e. if 40% positive means an expectation of 40% over repeated random draws)then 24% of the products are of the form (+)(+) and 24% are of the form (-)(-)so 48% of the products are positive

Hi ThereThanks for the replyYes I know that 48% is the expected value but the actual answer can be less or more than this number. So can we say something about the series if consistantly we are getting the actual number lower than 48% ?RegardsGaurav

Two possible causes:1. Non-independence: If the two series are correlated, the probability of a positive product will be different. For positive correlation, the probability will be higher. For negaitve correlation, the probability will be lower.2. Zeroes in the data set: The calculation that gets the 48% value assumes that the product of two non-positive numbers is positive. But if one or both non-positive number is zero, the product is not positive.

Hi Traden,Thanks for the reply. It helps me.Could you please provide some reading material on this?One more question: if the two series in question is say, price series and volume series then how can we exploit these two?RegardsGaurav

QuoteOriginally posted by: gauravkumar2Hi Traden,Thanks for the reply. It helps me.Could you please provide some reading material on this?One more question: if the two series in question is say, price series and volume series then how can we exploit these two?RegardsGauravYou can try to calculate liquidity. In Trade forum look a last one 'Local Volatility with Stochastic Interest Rates' in my formula and gardener3's comment.