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# Assign 2 - calculated(b calculate the probability that...

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Math 151, Spring 2011 Jo Hardin HW #2 Homework due on Thursday, January 27th, start of class. 1. DeGroot (3 rd or 4 th ed.), section 1.7: # 5, 8, 9, 10 2. DeGroot (3 rd or 4 th ed.), section 1.8: # 6, 7, 8, 10, 16 3. Additional problem in R: in 1994 a ﬂaw was discovered in the Intel Pentium chip, which produced an incorrect result when dividing two numbers. Intel initially announced that such an error would occur once in 9 billion divides, or “once in 27,000 years” for a typical user. As a result, they did not immediately oﬀer to replace the chip. What went wrong? If an error occurs “once in 9 billion divides”, then for one division, the probability that the event E (an error) is P ( E ) = 1 / 9000000000 and P ( E c ) = 1 - P ( E ) The probability of no errors in two divides (assuming that the probability of an error is independent) is equal to [1 - P ( E )] 2 and the probability of at least one error is 1 - [1 - P ( E )] 2 . (a) calculate the probability that there is a least one error when two divides are
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Unformatted text preview: calculated. (b) calculate the probability that there is a least one error when 1000 divides are calculated. (c) calculate the probability that there is a least one error when 1,000,000 divides are calculated. (d) calculate the probability that there is a least one error when 1,000,000,000 are calculated. Using R, generate a plot of the probability of at least one error over the range 10,000,000 to 1,000,000,000 along with a paragraph intended for the CEO of Intel discussing these results. Be sure to interpret the ﬁgure. (Hint: the R code: x = seq(0, 100, length.out=1000) y = 5*sin(x) + x plot(x, y, type="l", xlab="X axis", ylab="Y axis") title("a silly plot") text(60, 35, "here’s some text") will generate a plot of the function f(x) = 5sin(x) + x over the range 0 to 100)....
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