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In Exercises 1–8, use Bayes’ theorem or a tree diagram to calculate the indicated probability. Round all answers to four decimal places. [HinT: See Quick Example 1 and Example 3.]
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Finite Mathematics and Applied Calculus (MindTap Course List)
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- The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(4X+ 3) and variance V(4X+3)arrow_forwarda) Let X be a random variable and let E[X] =marrow_forward(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.arrow_forward
- An investment firm offers its clients municipal bonds that mature after several years. Since the cumulative distribution function of T the number of years to maturity of a randomly chosen bond, is img Calculate the following probabilities P(T>3)= ? P(1.4<T<6)=?arrow_forwardRefer to Exercise 15. Let E1 be the event that the wafer comes from Lot A, and let E2 be the event that the wafer is conforming. Are E1 and E2 independent? Explain.arrow_forwardMendel found no dominance in snapdragons, with one red gene and one white gene producing pink-flowered off-spring. These second-generation pinks, however, still carry one red and one white gene, and when they are crossed, the nextgeneration still yields the Punnett square from Exercise 87.Find each probability.a. P(red)b. P(pink)c. P(white)(Mendel verified these probability ratios experimentallyand did the same for many characteristics other than flowercolor. His work, published in 1866, was not recognizeduntil 1890.)arrow_forward
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