1. Probability theory and mathematical statistics: if the random variables X and Y obey a two-dimensional...

 

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1. Probability theory and mathematical statistics: if the random variables X and Y obey a two-dimensional standard normal distribution and the correlation coefficient between X and Y is If the constants a, b satisfyE[exp (ax + by - (a² + b² +2 pab))] = 1, h(x,y) is a binary continuous function. Using the definition of a two-dimensional standard normal distribution and expectation, prove that the following equation holds. E[h(x + a + pb, y + b + pa)) = E [exp (ax + by - 12(a² + b² + 2pab)) h(x, y)] 1. Probability theory and mathematical statistics: if the random variables X and Y obey a two-dimensional standard normal distribution and the correlation coefficient between X and Y is If the constants a, b satisfyE[exp (ax + by - (a² + b² +2 pab))] = 1, h(x,y) is a binary continuous function. Using the definition of a two-dimensional standard normal distribution and expectation, prove that the following equation holds. E[h(x + a + pb, y + b + pa)) = E [exp (ax + by - 12(a² + b² + 2pab)) h(x, y)]