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Let U and V be two independent zero mean Gaussian random variables of variances 1/4 and 1/9 respectively. The probability P(3V < 2U) is

1. 4/9
2. 1/2
3. 2/3
4. 5/9

Correct answer: 1/2

Solution

The inequality 3V < 2U can be transformed into a standard normal variable comparison, leading to a symmetric distribution around zero. Since both U and V are independent Gaussian variables, the probability of one being greater than the other is 1/2.

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