100AHW2 - STAT 100A HWII Due next Wed Problem 1: If we...

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Unformatted text preview: STAT 100A HWII Due next Wed Problem 1: If we flip a fair coin n times independently, what is the probability that we observe k heads? k = 0, 1, ..., n. Please explain your answer. Problem 2: Prove the following two identities: ¯ (1) P (A|B ) = 1 − P (A|B ). (1) P (A ∩ B |C ) = P (A|B ∩ C )P (B |C ). Problem 3: Independence. If P (A|B ) = P (A), prove (1) P (A ∩ B ) = P (A)P (B ). (2) P (B |A) = P (B ). Problem 4: Suppose an urn has r red balls and b black balls. We randomly pick a ball. Then we put 3 balls of the same color back to the urn. Then we randomly pick a ball again. What is the probability that the second pick is red? 1 ...
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