Let Y1 and Y2 denote the proportions of two different types of components in a sample from a mixtureof chemicals used as an insecticide. Suppose that Y1 and Y2 have the joint density function given by2, 0syı s 1, 0 < y2 < 1, 0 < y1 + y2 < 10, elsewherefV1,y2) =(Notice that Y1+Y2 < 1 because the random variables denote proportions within the same sample.) FindP(Y1 < 3/4, Y2 < 3/4)P(Y1 < 1/2, Y2 < 1/2)

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Answered: Let Y1 and Y2 denote the proportions of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The value of the correlation r = (x,y) for the information would be: n = 8, Sum(x) = 609, Sum(y) = 504, Sum (x)^2 = 47995, Sum (y)^2 = 32954, and Sum (xy) = 395650 0.255 0.147 0.855 0.174
Let X and Y have joint PDFfX,Y (x, y) = 3x^2y + 3xy^2 if 0 < x < 1, and 0 < y < 1 0 otherwise.a) Find the covariance of X and Y .b) Find Var(X).c) Find the correlation of X and Y (X and Y have the same variance.)
Assume that a population of patients contains 30% of individuals who suffer from a certain fatal syndrome Z, which simultaneously makes it uncomfortable for them to take a life-prolonging drug X. Let Z = 1 and Z = 0 represent, respectively, the presence and absence of the syndrome, Y = 1 and Y = 0 represent death and survival, respectively, and X = 1 and X = 0 represent taking and not taking the drug. Assume that patients not carrying the syndrome, Z = 0, die with probability 0.5 if they take the drug and with probability 0.5 if they do not. Patients carrying the syndrome, Z = 1, on the other hand, die with probability 0.7 if they do not take the drug and with probability 0.3 if they do take the drug. Further, patients having the syndrome are more likely to avoid the drug, with probabilities p(X = 1|Z=0) = 0.9 and P(X = 1|Z = 1) = 0.6 . Based on this model, compute the joint distributions and for all values of x, y, and z. Present the following joint distributions in tables. [Hint:…
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The defending attorney Mr. Justin Case was interested in how a lengthy trial could affect howlong a jury would deliberate on a case (and see if he should just cut to the chase). He observed asample of courtroom trials and noticed the following:Days inTrial (X) 5 2 6 4 5 6 2 4 2 1 HoursDeliberation (Y) 4 4 1 3 1 3 9 2 3 7 5) Mr. Case’s client’s most recent case took 10 days to complete. How long should he \ predict the jury deliberation will take?
Let s = f(x, y, z) and x = x(u, v, w), y = y(u, v, w), z = z(u, v, w). To calculate which of the following pieces of data do you NOT need? ✔z(1, 3, 4) = 6 ✔y(1, 3, 4) = 7 zu (1, 3, 4) = 30 ✔x(1, 3, 4) = 8 ✓f (8, 7, 6) = 29 f(8, 7, 6) = 17 | f(1, 3, 4) = 13 yu (8, 7, 6) 16 ✔ ƒ(1, 3, 4) = = 18 Question Help: Message instructor Post to forum Submit Question əs du -(1, 3, 4),
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The edge roughness of slit paper products increases as knife blades wear. Only 1% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 5% of products slit with worn blades exhibit roughness. If 25% of the blades in manufacturing are new , 60% are of average sharpness, and 15% are worn , what is the proportion of products that exhibit edge roughness? Let R = edge roughness N = new blades A = blades with average sharpness W = worn blades What are the mathematical notation for the following values: 1% = 3% = 5% = 25% = 60%= 15% = Express the question in mathematical notation; The proportion of products that exhibit edge roughness* = *Express in rational number with 2 decimal places.

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