18. Suppose P(A) = 0.3 and P(AUB) = 0.5. Find P(B) under each of the following additional assumptions:(a) A and B are mutually exclusive events(b) A and B are independent events(c) P(A' U B') = 0.9(d) P(B) is as large as it can be under the original assumptions that P(A) = 0.3 and P(AUB) = 0.5.

Answered: Image /qna-images/answer/7d6590a2-779c-40e1-af4e-753fb3684e67.jpg

Answered: 18. Suppose P(A) = 0.3 and P(AUB) =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Find de for the Follewing Fund Lion S dox 9= [(5-x) (4-2x)
Shelly is a talented researcher who has just received a large (two-year) research grant. The universityallows Shelly to borrow and save (research) money at the interest rater= 0.2, and her utility fromconsumption (of grant money) in years 1 and 2 is given byu(c1,c2) =c31c2[whereMU1= 3c21c2andMU2=c31]. For this question, please use thefuturevalue form for Shelly’s budget and/orvaluations (e.g. supposep1= 1 +randp2= 1). (a)If Shelly’s research grant pays $8,000 this year and $8,000 next year, how should she allocateher consumption of grant money between the two years? (b)If Shelly could choose between the grant in part (a), and a different grant that would pay her$3,700 in the first year and $12,500 in the second, which would she prefer? (c)How would your answer to part (b) change if we allowed Shelly to borrow or save with nointerest (i.e. withr= 0%)?
(b) Prove the following statements: i. {r €R: x - 4| = 2|a| – 2} = {-6,2} ii. {x ER: |x – 4| < x} = (2, 00) iii. P(AN B) = P(A) N P(B). iv. P(A)U P(B) C P(AU B) 11. %3D || ch DELL P
Answer the ff.
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Suppose P(E) = 0.154, P(F)= 0.215, and P(F N E) = 0.074. What is P(F | E)?
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A supplier of paper produces 10-sheet packs of certain high gloss paper for the production of brochures. For a publishing project we need 205 sheets and so purchase 21 packs. Due to manufacturing imperfections the packs do not always contain 10 sheets. If we denote by X; the number of sheets of paper in the ith pack then (0.1 if k = 9 0.8 if k = 10 P(X₁ = k) = 0.1 if k = 11 0 if k {9, 10, 11}. We further assume that the random variables X; are independent. (a) Find the mean and standard deviation of Xi. (b) Denote by X the total number of paper sheets we have purchased, X = X₁++X21. Calculate the mean and standard deviation of X. (c) Estimate the probability that we have purchased enough sheets for our project, 205). You should use the continuity correction. i.e. P(X
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