Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.52, P(F) = 0.31, and P(ECF) =0.13. Calculate the probabilitiesbelow.P(EC)0.48(a)P(En F) =.18(b)P(E U F) =0.83(c)P(ECn F(d)=P(EUF(e)

Compute the probability as follows.

Answered: Let E and F be two events of an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let Y = the number of days on which the train arrives on time. What is P(Y = 4)? Interpret this value. (0.90)4 (0.10)². There is a 0.66% probability that exactly 4 of the 6 trains arrive on time. (0.90) ¹ (0.10)². There is a 0.66% probability that at least 4 of the 6 trains arrive on time. This probability cannot be calculated because this is not a binomial setting. O()(0.90)+ (0.10)². There is a 9.84% probability that at least 4 of the 6 trains arrive on time. O()(0.90)4 (0.10)². There is a 9.84% probability that exactly 4 of the 6 trains arrive on time.
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Exercise 4. A certain species of plant always has either three or five leaves. The number is random, with P(3 leaves) 0.4 and P(5 leaves) = 0.6. Each plant has a flower which, randomly, is either open or closed, with probabilities P(open) = 0.8 and P(closed) = 0.2. A botanist collects 1000 randomly chosen plants from this species and nds the following distribution of traits: open closed N3,closed 3 leaves N3,open 5 leaves NE,open N5, closed a) Assuming the two traits are independent, determine the expectations of the counts №3,open, N3,closed, N5,0-en, and N5,close in the table. b) Determine an approximate value for the probability P(N3,open > 340). Exercise 5. Assume that we have observed the following values from a normal distribution with known variance o2 = and unknown mean . 1.23 -0.67 1.16 1.67 0.24 2.99 0.02 .17 0.27 21. Test the hypothesis Ho: = 0 against the alternative H₁: #0 at significance level a = 5%. Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on…
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Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.52, P(F) = 0.31, and P(EC F) =0.13. Calculate the probabilities below. P(EC)0.48 (a) P(En F) = .18 (b) P(E U F) =0.83 (c) P(ECn F (d) = P(EUF (e)