# errors

1. ### Limit as x approaches zero

(1) Compute the limit for p(x) = x^2 - 1. lim p(p(p(p(x)))) as x approaches 0. (2) Find all the errors in the following incorrect string of equalities. (a) lim 1/x as x approaches 0 = lim x/x^2 as x approaches 0 = (lim x as x approaches 0) (lim 1/x^2 as x approaches 0) = 0 . ? = 0. (b) lim...
2. ### fitting with individual errors in data

I have two sets of data x and y with individual errors dx and dy. I want to plot a linear line through the data of the form y=ax+b that takes into account the individual errors in x and y and translates this to an error in the fitting parameters a and b. Is there any method to do this?
3. ### Cholesky Roundoff Errors

I am developing a Cholesky algorithm in C++ (a computer language ) and I am using single precision, 32bits. I read that if my matrix is ill conditioned then the main diagonal may turn negative due to round off errors. I can understand that it might be zero, but could someone give an example...
4. ### Help plz with integral approximation error calculation finding K

I'm working on integral approximations and errors. My errors never come out right. My approximations are correct, so I think I'm just misunderstanding how to find K. Q.a) Find the approximations T8 and M8 for ∫(0 to 1) cos(x2)dx I found these to be T8=0.902333 and M8=0.905620 b) Estimate...
5. ### Calculation of type II errors

I am given: $n_1 = 50, \overline{x}_1 = 2.61, s_1 = 0.12$ $n_2 = 40, \overline{x}_2 = 2.38, s_2 = 0.14$ H0 is to be rejected if and only if $\mu_1 - \mu_2 = 0.20$. I need to find $\beta$, the probability of a type II error (false acceptance of H0), when $\mu_1 - \mu_2$ is 0.12 and then 0.16...
6. ### Dealing with subtracting means with margin of errors

Hi all, If i have two means with a margin of error (95% confidence intervals). how can I subtract one from the other, what will the computed margin of error be? e.g. (10 +/-2) - (8 +/-1) Many Thanks
7. ### Type 1 and 2 errors for binomial

I am working on a research project this summer and I'm a bit confused about type 2 errors. The actual scenario I am testing is nonsense to most people so I'll rephrase the problem in a way that makes more sense. There is a bag containing many green balls and 1 red ball. A boy comes to play a...
8. ### Simple Regression - Assessing SSE (sum of square errors)

Hello, I can't figure out how to solve this question: Consider these summary statistics for a random sample: Mean of x=20 Mean of y=10 Sx(variance)=3 Sy=7 Sxy= -18 For which of the following straight lines would the SSE (sum of the squared errors) be SMALLEST? a) y= 4 -6x b) y= 8-6x c) y=...
9. ### Theory of errors and confusion with roundings

With given: k_1 = 37.1\pm0.3 k_2 = 9.87\pm0.11 k_3 = 6.052\pm0.016 estimate the absolute and relative error for w = k_1 \cdot k_2^2 \cdot k_3^3 and round both w and the error in such a way not to lose any precise figures. So my attempt looks like this: We know the absolute errors for the...
10. ### Algebraic Errors

This is sample work of factorising with fractions in an inequality. I've been told that the 3rd line is incorrect, as a^2+b^2 cannot be factored over a real number. Can anyone help me determine if the factoring simply stops at the second line, or is there a correct way to continue? Many...
11. ### Identify errors

Hi guys, the task: Identify the errors a stundent made in the following problems and correct them. Explain your answer. 1. (7x)^1/3 = 1 divided by 7x^3 my answer: it should be = (7x)^1/3 = 7^1/3 x^1/3 Is that right? 2. 2^2 divided by 2^1/4 = 2^2/4 = 2^1/2 = square root of 2 What is wrong...
12. ### Normality plot (no of errors over 2 years)

I am trying to analyse number of errors over a period of 2 years and I run a normality test for my data via minitab. it shows Can i conclude that the graphical representation show non-normal data ? then what should i do ? Thanks!
13. ### Linear codes: how to construct checkmatrix, localise errors

The problem goes like this. A linear binary code is given by the control matrix H = 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 a) What codeword can, with at most one error, become 010110? b) Find a word that cannot arise with at most one error in a codeword. First, I don't understand how to...
14. ### probability of DNA sequence errors

I am a molecular biologist with a probability question. Before I get to the question, I will give you a little background information about DNA. As you may know, DNA consists of two long polymers of simple units called nucleotide bases (4 types: A, C, G or T) arranged in an antiparallel double...
15. ### Residuals vs. errors

What is the difference between a residual and an error?
16. ### Correcting errors

Given an error rate and a binary (n,k,d) - code I can find out the probability of making a certain number of errors but how do I work out the probability of correcting such errors if I don't know what the codewords are?
17. ### Probability that 2 errors occur on separate lines

Hi, I have the following problem, but I am stuck on question D. I would really appreciate if someone could give me a hand! I know I have to use Bayes' theorem, but I don't know how :/. Thanks! The problem says: "A page of typescript contains 40 lines, with 80 characters per line. Each...
18. ### Deflection of beam. Efect of % errors in span and load data.

OK so I'm practicsing some of the questions out of my text book for when I start my course in 2 weeks and finding this one pretty difficult, but here it goes. Bestend Properties is refurbishing an old hospital that was built in the 1950's. The building's main structure is a steel frame. The...
19. ### Using the normal approximation interval to calculate number of errors

Hello I have a bit of a problem how to use the normal approximation interval( Binomial proportion confidence interval - Wikipedia, the free encyclopedia ). I would be very happy if anyone could explain further! I am trying to calculate the upper probability of an error, say I have a confidence...
20. ### Type 1 and Type 2 Errors

Hello, I was given the following handout: I know how to get the power, because this is 1 - beta = 1 - .40 = .60. But I just don't get how beta was calculated using the above figures. Plus, if I have the following problem: A sample size of 102 will be sufficient to detect an effect size...