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probabilities of random variables

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Inspired by 6.4.7 from the text: Let X1 and X2 be indicators of independent

events with probabilities p1 and p2, respectively. Consider random variables Y = (X1 + X2) and Z = (X1 − X2). Prove your answers to the questions below.

1. (5pt) For what values of p1 and p2 will Y and Z be uncorrelated?

2. (5pt) For what values of p1 and p2 will Y and Z be independent?

 
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