Question

Problem 1. A biased coin with probability plandin with a Heads is lipped 4 times. (a) Define the basic random variables and give the sample space and assign probabilities to the outcomes. (b) Let X be the total number of Heads in the four flips Draw a Venn diagrain showing the five events X = ii 0,1,2,3,4 as well as the sample space and the outcomes. Is X a random variable? c) Are the events X 1 and X 2 disjoint? Are they independent? What about the events X-1 and X2 (d) Let Y be the first flip when a Heads appears and Y-oif there is no Heads in the four flipe. Draw a Venn diagram showing the five eventsY,0, 1,2,3,4 as well as the sample space and the outcomes. (e) Are the events X-3 and Y-4 disjoint? Are they independent? I low about the events X = 2 and Y-2? Disjoint? Independent?

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