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Two independent random variables X and Y are uniformly distributed in the interval [-1,1]. The probability that max[X,Y] is less than 1/2 is

1. 3/4
2. 9/16
3. 1/4
4. 2/3

Correct answer: 9/16

Solution

The probability that both X and Y are less than 1/2 can be calculated by considering the area of the square formed by their uniform distributions. Since both variables are independent and uniformly distributed over the interval [-1, 1], the area of the region where both are less than 1/2 is (1/2 + 1)(1/2 + 1) = (3/2)(3/2) = 9/16 of the total area of the square, which confirms that the correct answer is 9/16.

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