1. K

    Standard deviation on scaling of random variables

    I have the answer already (based on simulations), but want to know exactly which theorem/ law is at play: Suppose X1, X2, X3, X4 are 4 positive random variables such that X1+X2+X3+X4=1. Suppose I scale them with known constants C1, C2, C3, C4, respectively, then look at the function below...
  2. S

    Mean of means - standard deviation of mean values

    Sorry if this has been asked numerous times and sorry if I describe it from an engineers point of view. Let us say I have N measurements and I calculate the mean value and the standard deviation. Okay. Now let us have M times N measurements. I could calculate now the mean value of the whole...
  3. O

    Criticism of the Standard Deviation

    Standard Deviation is widely used to measure risk in assets. I think a higher standard deviation is considered a risky bet, with greater upside and downside potential. However, if the asset A's returns are: 50, 50, 50, 400 and Asset B's return are 50, 50, 50, 50 -- the latter will have much...
  4. H

    Confidence interval for the population standard deviation?

    Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation. Assume that the population has a normal distribution. The hockey coach selected eight players at random and timed how long each player took to finish their exercises. The...
  5. E

    Standard Deviations and Standard Deviations of Reciprocals

    If the standard deviation of A, B, and C is greater than the standard deviation of X, Y, and Z, what does that say about the standard deviation of 1/A, 1/B, and 1/C compared to the standard deviation of 1/X, 1/Y, and 1/Z? A, B, C, X, Y, and Z are rational numbers > 1.
  6. J

    Unbiased Estimator of the Standard Error of another Estimator

    Suppose that $Y_1,...,Y_n$ is an IID sample from a uniform $U(\theta, 1)$ distribution. The method of moments estimator for $\theta$ is $\tilde \theta=2\bar Y-1$. The standard error of $\tilde \theta$ is $$\sigma_{\tilde \theta}=\frac{1-\theta}{\sqrt{3n}}$$ Find an unbiased estimator of...
  7. L

    Why use variance instead of standard deviation?

    This drives me crazy, The question is simple: A manufacturing process has the expected value of 200minutes and standard deviation of 10minutes The reset process has the expected value of 30 minutes with the standard deviation 3 minutes Compute the probability that the sum of the...
  8. J

    Manipulate data to match given mean and standard deviation

    I have a set of data with a mean of 55.05 and a standard deviation of 7.51. However, I want to transform these data to a list of values with a mean of 55.62, a standard deviation of 58.69, and the list should not contain negative values. Is this possible? Thank you The list of data is below...
  9. B

    Find standard deviation given normal probability

    I have $X \sim N(0,\sigma^2), Y \sim N(-1,4) \mbox{ independent}, \\ Z = X-Y$ find $\sigma$ such that $P(Z \le 7) = 0.84134$ what I have done is : $X-Y \sim N(0-(-1), \sigma^2+4) = (1, \sigma^2+4)$ $\begin{array}{lcl}P(Z \le 7) & = & P( \frac{Z -1}{\sqrt{\sigma^2+4}} \le...
  10. P

    What is the Standard Error Significance?

    Hi, I'm having a hard time really understanding what Standard Error is, why it's important and perhaps more importantly how to interpret the result. Or "Ok I have the result, what is it telling me about the data?"
  11. I

    Standard and standard deviation

    Hello :) I have 2 questions which i didn't succeed to solve them, I don't even have a direction, so can you help me please? The following given refers to 2 questions - The standard is that the weight of a cheese should be between 94 to 106 grams. 1. The industry produces cheeses, the...
  12. S

    Which of the two sets of data intervals has the greater standard deviation?

    A company is evaluating two employees' times to complete the same repetitive task. Employee A's time and frequency Under two minutes: 2 2 to 3.99 minutes: 6 4 to 5.99 minutes: 9 6 to 7.99 minutes: 2 8 to 9.99 minutes: 1 Employee B's time and frequency Under two minutes: 3 2 to 3.99 minutes: 5...
  13. F

    Convert vertex form to standard form

    Hi, I have a parabola with the following vertex info, I am trying to convert this to standard form (ax2 + bx + c), however I cannot seem to get the conversion correct. I have plots for the parabola and have created a trend line with equation in excel so I can compare and be confident my...
  14. L

    One measure significant in standard deviation?

    When is one observation not considered statistically significant, such as subtracting one (Bessel's correction) while calculating standard deviation?
  15. P

    Why is my Standard Deviation larger than the mean?

    Hello, I have an assignment asking me to calculate the mean and standard deviation for Weekly housing cost. All of the data came from 306 students who filled in the survey. I was given raw data in excel. I used excel to calculate the mean by typing '=average(' into the formula bar and...
  16. V

    Convert LaTeX to Standard Online Notation

    Does anyone know of a software or preferably an online tool that can convert LaTeX into standard online mathematical notation? \left(-\frac{\left(x^2-\pi x-\pi ^2\right)^3}{3\pi ^5}\right)-\frac{\pi }{3} I would like to find some sort of online tool that can convert this into something...
  17. G

    Standard Normal Distribution

    $Z$ ~ $N$(0,1) How to show that $Z\stackrel{d}{=} -Z$ and $\frac{Z^2}{2}$ ~ gamma($\frac{1}{2}$)? Also how to show that only the standard normal distribution satisfies these 2 properties? In other words, if you have $Z\overset{d}{=} -Z$ and $\frac{Z^2}{2}$ ~ gamma($\frac{1}{2}$), then $Z$ ~...
  18. B

    Standard Deviation

    What is approximate standard deviation for the list of numbers: 10.4, 9.8, 10.0, 9.2, 10.5, 9.8, 9.9, 10.1, 10.4, 10.2, 10.7, 9.6? A. 2.1 B. 1.9 C. 1.75 D. 1.8 The question shows up on my kid's test recently. The standard deviation is 0.42. Why can the answer be C. 1.75? If 0.42...
  19. S

    Conic Section Parabola Standard Form

    Can someone check my work? If I did wrong please explain to me how to do it right? I only googled how to do it and that's how I've come up with that answers, based on this..
  20. G

    Dividing Standard deviation by sqrt(n)

    Hi all, I've been arguing with a mate about a thing he calls Real Standard Deviation. What he does is siply dividing the standard deviation of a set of data by the square root of the number of observations, n. Now, I myself couldn't find any information about it on google, and can't really...