Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.7, Pr(B) = 0.5, Pr(C) = 0.25.1. Find Pr(A). Pr(B'), and Pr(C').Pr(A')Pr(B)Pr(C')=2. If Pr(AU B) = 0.75., find Pr(An B).Pr(An B) =3. Suppose that we know that B and C are disjoint events. Find Pr|BUC.Pr[BUC4. Suppose that instead of being disjoint C C B. Find Pr BUCPr[BUC =

To compute the required probabilities

Answered: Assume that A, B, and C are subsets of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let x be a random variable that represents the weight of a lion in a certain region of Africa. Assume that x is normally distributed with a mean = 260 lbs . With standard deviation =30 lb Please include the graphs for questions A and B
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Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.8, Pr(B) = 0.6, Pr(C) = 0.15. 1. Find Pr(A'), Pr(B'), and Pr(C'). Pr(A') = Pr(B') = Pr(C') = 2. If Pr(A U B) = 0.85., find Pr(AN B). Pr(AN B) = 3. Suppose that we know that B and C are disjoint events. Find Pr[BUC. Pr[BUC] = 4. Suppose that instead of being disjoint C C B. Find Pr[B U C]. Pr[BUC] =
9. Let 7 = 1.135013 be the sample mean of an iid sample r1,..., T50 from a gamma population Gamma(1, 3). Here ß > 0 is the unknown paramcter of interest. Construct an approximate 95%-CI for ß.
12. Let (*1, 12, ., r„) be independent samples from the uniform distribution on [0,0]. Let X(n) and X(1) be the maximum and minimum order statistics respectively, (a) Find the distribution of X(m) and X(a) and hence, their means and variances. X{n) (b) Show that 2nY x where Y = – In %3D (c) Show that 2) In - Xản: Hence write a function of the geometric mean, i=1 (II GM(r) = which is Xn 1
7. (4 pts) if fx(x) = 2x for 0 ≤ x ≤ 1 and Y = 10 – X², then find Fx (x) (remember to give the sample space).
5. Let (*1, x2, .., rn) be n independent random sample of size n from a uniform distribution on the interval [01,02]; (a) find the c.d.f of, X(1), the minimum order statistic (b) find the c.d.f of, X(n), the maximum order statistic (c) Hence, find the mean and variance of X(1) and X(n)-

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