Two fair coins are tossed. Let X 1 be anindicator of heads on coin 1 and let X 2

Question

Two fair coins are tossed. Let X1 be anindicator of heads on coin 1 and let X2 be an indicatorof heads on coin 2. a. Determine the probability mass function for X1 +X2.   b. Determine the probability mass function forX1X2. c. Show that X1X2 andX21 aren't identically distributed eventhough X1~X2. Two fair coins are tossed. Let X1 be anindicator of heads on coin 1 and let X2 be an indicatorof heads on coin 2. a. Determine the probability mass function for X1 +X2.   b. Determine the probability mass function forX1X2. c. Show that X1X2 andX21 aren't identically distributed eventhough X1~X2. b. Determine the probability mass function forX1X2. c. Show that X1X2 andX21 aren't identically distributed eventhough X1~X2. c. Show that X1X2 andX21 aren't identically distributed eventhough X1~X2.

Explanation / Answer

There are 4 different possible outcomes: HH, TT, HT, andTH a) The pmf for X1+X2 is: X1+X2 = 0, p = 1/4 = 0.25 (we need to have TT) X1+X2 = 1, p = 2/4 = 0.50 ( we can have TH or HT) X1+X2 = 2, p = 0.25 (we need to have HH) b) The pmf for X1X2 is: X1X2 = 0 , p = 3/4 = 0.75 (We can have TT, HT, or TH) X1X2 = 1, p = 1/4 = 0.25 (We need to have HH)

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