Mathematics > QUESTION PAPER (QP) > Georgia Institute Of TechnologyMATH 3670math3770 Practice Test (All)
Georgia Institute Of TechnologyMATH 3670math3770 Practice Test
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Practise Final for math3670 0) Good luck & have a great Holiday! :) 1) Prove that E[X + Y ] = E[X] + E[Y ] where X and Y are random variables. 2) We flip the same coin 3 times independently. On one... side of the coin there is a 2 and on the other side a 1. Side 2 has probability 0.2 whilst side 1 has probability 0:8. Let Xi designate the result of the i-th trial. Hence X1, X2 and X3 are i.i.d. and P(Xi = 2) = 0:2 ; P(Xi = 1) = 0:8 We build the product of the three values obtained. Calculate the probability that the product is equal to 4. Hence calculate the probability: P(X1 · X2 · X3 = 4). 3) Let X be a continuous random variable with density function f(x) = cx3 for x 2 [0; 1] and 0 outside the interval [0; 1]. a) Determine the value of the constant c. b) Calculate P(X 2 [0:5; 1 [Show More]
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