There is a fair coin and a biased coin that flips heads with probability 1/4. You randomly pick one of the coins and flip it until you get a heads. Let X be the number of flips you need. Compute EIXL and Var[Xl. 2.
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- ProbabilitySolve c,dThe probability that a student will pass in the Economics test is 2/3, and that a vill not pass in the English test is 5/9. If the probability of his passing in at ne ane of these two tests is 4/5 , find the probability that he will pass in both 20 is the tests. CS Scanned with CamScanner
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- Use the Hypergeometric formula: A high school graduation committee is to be formed by choosing randomly from 11 students and 5 teachers. If the committee is to have 8 members, find the probability that exactly 6 of them are students.A large bag contains pretzels with 3 different shapes: heart, square, circle . Billy plans to reach into the bag and draw out one pretzel at a time, stopping only when he has at least one pretzel of each type. Let the random variable X denote the number of pretzels that Billy will draw from the bag. You can assume that there is an infinite number of pretzels in the bag with equal proportions of each shape. Find E(X).EXS: Un fair tossing A coin which has which has probability p of coming up Heads is tossed three times - Levt X b the Heads observed. what is p(x=1) ? number of 2 a. 3C1-p/p ² 2 6₁ PCI-p] ² C - None of the other choices d 2. 318 3 (1-P) P