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  1. R

    Geometry

    Think about the triangle inequality.
  2. R

    Time Series: Partial Autocorrelation Function (PACF)

    Subtract the known constant from each term of the series and proceed. The level of the time series does not enter into the relationship between lags.
  3. R

    brownian motion in stopping time

    Since BM has continuous sample paths, and variance equal to t (in your formulation), it would seem that |W(\tau_n)| = n, almost by definition. There may be a tacit assumption that n is an integer, but that doesn't appeaqr necessary because of path continuity.
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    Paired t-Test by comparing 2 set of mean/median

    You would be better off if everyone played the same game.
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    Need help with algebra word problem (headwind/tailwind)

    Try adding and subtracting your equations.
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    Packaging of virus particles (Probability)

    You need to evaluate the following: \sum 12!/x_1!...x_8! where the sum goes over all possible combinations so that each x_i is at least 1, and \sum x_i is at least 8. Then multiply the result by (1/8)^{12}. For example, there are 8 ways that exactly one x_i contains 2, with the other 7...
  7. R

    Packaging of virus particles (Probability)

    Most likely someone employed an approximation to the multinomial distribution. it is possible to calculate such a probablility exactly using a computer program, but it is somewhat involved. It is essentially a problem in combinatorics.
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    Outlier and Pearson corellation of coefficient

    If you suspect an outlier, you are better off with the median, independent of other distributional assumptions. One outlier can severely distort the correlation coefficient. This is one reason you should always graph your data in some form or fashion. However, you cannot compute a reliable...
  9. R

    i am stuck

    FIrst, integrate the differential equation and use the initial condition for the constant to find the volume.
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    Help with Trig

    Start by writing the left hand side in terms of sine and cosine.
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    Help with Trig

    Use the definition of tangent.
  12. R

    Simple Linear Regression

    \sum (x_i-\bar x)(y_i-\bar y) = \sum (x_i-\bar x)y_i- \sum (x_i-\bar x)\bar y. The second sum is zero.
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    Simple Linear Regression

    If you expand each sum, you will find out they are the same. Only one of the variables needs to be centered.
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    two lines intersect

    If the point is on the y-axis, you know what the x-coordinate is.
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    How to look for the critical value of Pearson Correlation?

    Re: How to look for the critical value of Pearson Correlatio If you can compute t-distribution critical points, you can use t = r \frac{\sqrt{n-2}}{\sqrt{1-r^2}} which has a t-distribution with n-2 degrees of freedom.
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    I need help with a radical equation

    Start by factoring a perfect square.
  17. R

    Multiple Regression, No Understanding

    You should review the online help for the Excel function LINEST.
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    need help with this problem

    Raise 1.08 to the 20th power first.
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    Extending of given sequances

    To generate random samples from the bivariate normal distribution, do the following. Generate Z_1, Z_2 as standard normal variates. Then let X = \mu_1 + \sigma_1 Z_1, Y = \mu_2 + \sigma_2 ( Z_1 \rho + Z_2 \sqrt{1-\rho^2} }).
  20. R

    Sum to product and product to sum

    The cosine is an even function; the sine is an odd function.
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