Multiple choice

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. ¾

  2. 9/16

  3. ¼

  4. 2/3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

X and Y are uniform on [-1,1], so PDF is f(x) = 1/2 on this interval. We need P(max(X,Y) < 1/2) = P(X < 1/2 AND Y < 1/2). Since independent: P(X < 1/2) = (1/2 - (-1)) / 2 = 1.5/2 = 3/4. Same for Y. P(max < 1/2) = P(X < 1/2) × P(Y < 1/2) = (3/4) × (3/4) = 9/16. The interval from -1 to 1/2 has length 1.5, and the total interval length is 2, so probability is 3/4 for each variable.

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