Introduction to Probability · Problem 4.1.35

Conditional Probability — Grinstead & Snell

Mathematics — Probability · independence-random-variables

Problem

A box has numbers from 1 to 10. A number is drawn at random. Let X1X_1 be the number drawn. This number is replaced, and the ten numbers mixed. A second number X2X_2 is drawn. Find the distributions of X1X_1 and X2X_2. Are X1X_1 and X2X_2 independent? Answer the same questions if the first number is not replaced before the second is drawn.

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