Answered: 4.3 The following pattern classes have… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

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4.3 The following pattern classes have Gaussian probability density functions:
w:{(0,0), (2,0), (2, 2), (0, 2)) and w₂:{(4,4), (6,4), (6, 6), (4, 6)¹}.
(a) Assume that P(W₂₁) = P(W₂) =
2
boundary between these two classes.
(b) Sketch the boundary.
and obtain the equation of the Bayes decision

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
(a) The following pattern classes have Gaussian probability density functions. w; = { (0, 0)", (2, 0)" , (2, 2)" , (0, 2) "} and w2 = { (4, 4)" , (6, 4)" , (6, 6)", (4, 6)" } (i) 1 Assuming that p(w;) = p(w2) = 2 obtain the equation of the Bayes decision boundary between these two classes. (ii) Sketch the boundary.
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|A| Question 11: Suppose that 2 = {HHH,HHT,HTT,TTT}, x = 2° and r(A) . Now, let Ybhe a random -3 for w = HHH variable on the probability space [N,A, P] defined by: X(@) = 1 for o = HHT,HTT for a = TTT Then: 09+ 0.5 0,7- 0.6+ a) Represent this random variable graphical. 0.4- 03- 02+ 0.1+ for z<-3 for - 3sz<1 for 1Sr<2 b) Determine the event in the relation: {@ e N ;X(@) S z} = for z22 c) Determine the distribution function F, and sketch it. 0.9- 0.5- 0.7- 0.6- 05- 0.4+ 03- 02+ 0.1+ F(2) = Question 13: A factory produce a kind of light bulbs. It claims by 95% confidence level, that the mean lifetime of the lamps has u = 500 hours working with standard deviation o =5 working hours. We select a sample of 36 bulbs and find that the mean lifetime of the lamps equal to 480 hours working. Then: a) Determine 95% confidence interval for the mean lifetime. (The standard nurmal distribution table is on the next page). b) If the sample size equal to 100, what is the value for the margin error 6, ?…
6) The joint probability density function of two random variables, X and Y is given by 1² – 2pxy + y² 202 - 00
(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) or

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