2. (a) Two events E, and E, associated with a sample space of an experiment are such that P(E,) = 0.27 , P(E,) = 0.40 and P(E, U E,) = 0.58 . Determine whether E, and Ez are independent. Two events A and B are such that, they are independent and P(A) = x and P(B) = x + 0.2 and P(A n B) = 0.15 . Find (b) i) the value of x P(AU B) and P(A° /B“) , where A° ,Bº are the complements of events A and B respectively. ii)

2. (a) Two events E, and E, associated with a sample space of an experiment are such that P(E,) = 0.27 , P(E,) = 0.40 and P(E, U E,) = 0.58 . Determine whether E, and Ez are independent. Two events A and B are such that, they are independent and P(A) = x and P(B) = x + 0.2 and P(A n B) = 0.15 . Find (b) i) the value of x P(AU B) and P(A° /B“) , where A° ,Bº are the complements of events A and B respectively. ii)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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H3.
7. Let A and B be two events from the same sample space with P(A) = 0.35 and P(B) = 0.70. (a) Is it possible that the events A and B are mutually exclusive? Fully justify your answer. (b) Suppose that P(A|B) = 0.2, find P(An Bc) (fully justify your answer analytically). (c) Is it possible that P(A|B) = 0.60? Justify your answer analytically.
4. (4.1-8). In a smoking survey among men between the ages of 25 and 30. 63% prefer to date nonsmokers, 13% prefer to date smokers, and 24% dont care. Suppose nine such men are selected randomly. Let X equal the number who prefer to date nonsmokers and Y equal the number who prefer to date smokers. (a) Determine the joint pmf of X and Y. Be sure to include the support of the pmf. (b) Find the marginal pmf of X. Again include the support.
3. (Competing patterns among coin flips) Suppose that Xn, n > 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = }. (These are just i.i.d. fair coin flips.) Let A = (a1, a2, a3) = (0, 1, 1), B = (b1, b2, b3) = (0,0, 1). Let TA = min(n 2 3: {Xn-2, Xn-1, Xn) = A} be the first time we see the sequence A appear among the Xn random variables, and define TB similarly for B. Find the probability that P(TA < TB). (This is the probability that THH shows up before TTH in a sequence of fair coin flips.)
Consider the sample space S={ copper, sodium, nitrogen, potassium, uranium, oxygen, zinc), and the events A=[copper, sodium, oxygen) B=[sodium, nitrogen, potassium, zinc) C= (oxygen, nitrogen} Match column 1 to column 2 Prompts Submitted Answers A' {nitrogen, potassium, uranium, zinc) AUC {copper, sodium, oxygen, nitrogen)} B' and C Choose a match ANBNC (AnB') UC' Choose a match
Suppose data is obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.80. (a) Test the hypothesis that Ho: p = 0 against H₁ :p #0 with a = 0.01. Reject the null hypothesis. (b) Test the hypothesis that Ho: p = 0.25 against H₁: p = 0.25 with a = 0.01. Reject the null hypothesis. (c) Construct a 99% two-sided confidence interval for the correlation coefficient. Round your answer to 3 decimal places. < p < i i
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3b)
10.STATISTICAL INFERENCEQuesdtion 3 d
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