3. Suppose that X is uniformly chosen from {1,2,3} and (Y | X = k) ~ Binomial(2, 4). We have a 4-sided die, and paint X of its faces red, leaving the rest white; X is uniformly chosen from {1, 2, 3}. Then we roll the die twice, and let Y be the number of times a red face comes up. In other words, (Y | X = k) ~ Binomial(2, 4). Give the following in the form of a table: (a) Pyx (ba), the conditional PMF of Y given X. (b) Pxy (a, b), the joint PMF of X and Y. (c) Pxy (a | b), the conditional PMF of X given Y. (d) Finally, explain what the X = 1, Y = 1 entry of your table in (c) means, in reference to the die with painted faces.
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- Suppose that 2 balls are randomly selected (without replacement) from an urn containing 3 red, 4 blue, and 5 white balls. If we let X and Y denote, respectively, the number of red and white balls chosen. Solve for P(X=2).For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)…
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