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Min-Max Conditional Probability — MeetProba

Exercises/Continuous Distributions

Min-Max Conditional Probability

Min-Max Conditional Probability

Easy

Exercise 1 / 9

Answer

Let $X_1$ and $X_2$ be IID random variables with uniform distribution on $[0, 1]$ . Define:

Y = \min(X_1, X_2), \quad Z = \max(X_1, X_2)

What is $P(Y \geq y \mid Z \leq z)$ for any $y, z \in [0, 1]$ with $y \leq z$ ?

2

)

y

≤

z