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    Intuitive reason absolute values are used for transformations in statistics?

    or did you want a specific case? say X~U(0,1), and I want to know say Y=X-1. then I can say g-1(y)=y-1., and d/dy g-1(y)=-y2, so then my distribution of Y would be f(g-1(y))|d/dy g-1(y)|=y-2. I get that if we didn't take the absolute value, then this function would be negative... But...
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    Intuitive reason absolute values are used for transformations in statistics?

    well, if say X distributed as f(X), and say i have Y=g(X), and I want to know the distribution of Y, in a simple case I can say that Y~f(g-1(y))|d/dy g-1(y)|. I don't know why we'd always want the absolute value, as opposed to the derivative in general.
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    Intuitive reason absolute values are used for transformations in statistics?

    Homework Statement Homework Equations The Attempt at a Solution this isn't really homework, but I was just wondering if someone could offer an intuitive reason as to why when random variables are transformed, we use absolute values of derivative of those functions, as opposed...
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    Expected value and variance of a conditional pdf (I think I have it)

    Awesome, thanks. This concept took me a little while to get, but I think I got it. It's not very hard, but my book is kind of vague.
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    Using Chebyshev's Theorem (and another minor question)

    the fact that P(A) + P(B) > 1 tells you there has to be some overlap, right? So you're looking at kind of a best case/worst case scenario. How small could the overlap be? How large could the overlap be?
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    Integration of random variables

    well, if it's conditional, and it's dependent on x, shouldn't your outcome be a function of x?
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    Using Chebyshev's Theorem (and another minor question)

    regarding your second question, just something to think about: what is P(A Union B)? what does this tell you about P(A intersect B)?
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    Expected value and variance of a conditional pdf (I think I have it)

    Homework Statement Suppose the distribution of X2 conditional on X1=x1 is N(x1,x12), and that the marginal distribution of X1 is U(0,1). Find the mean and variance of X2. Homework Equations Theorem: E(X_{2})=E_{1}(E_{2|1}(X_{2}|X_{1}))...
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    Poisson distribution questions

    I could be wrong on this, so take this with a grain of salt. Apply the definition of expected value. It looks like you could rewrite your term as x!/(x-12)! Does this help? Then when you take the sum, the x! should cancel, and you'll be left with (x-12)! on the bottom.
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    Find dy of x/( sqrt (3x + 6) )

    when you have functions like this, sometimes it's easier to write out your systems in general terms. rewrite your equation as f(x)/g(x), or f(x)g(x)^-1, if you prefer, where f(x)=x and g(x)=√(3x+6). so now find the derivative of this. do it piece by piece until you have your solution.
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    Finding convergence of a recursive sequence

    what is the first thing you think of when you see "n+1"?
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    Finding a marginal pmf

    Thanks. As far as the latex goes, I usually type it in an editor, and then paste the code in here.
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    Finding a marginal pmf

    okay, so finally, we have that f_{1}(x_{1})=\sum_{i=x_{1}}^{\infty}p^{2}q^{i}=p^{2}\sum_{i=x_{1}}^{\infty}q^{i} so \sum_{i=0}^{\infty}q^{i}=\dfrac{1}{1-(1-p)}=\dfrac{1}{p}. \sum_{i=0}^{x_{1}}q^{i}=\dfrac{1-q^{x_{1}-1}}{1-q}=\dfrac{1-q^{x_{1}-1}}{p}, so taking the difference, we have...
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    Finding a marginal pmf

    Okay, so looking at a picture, I know that P(x1,x2)=0 whenever x1>x2 (and x1,x2>0). So I have kind of a triangular set up. So looking at these values, then, I'm thinking that my marginal for x should be f_{1}(x_{1})=\sum_{i=x_{1}}^{\infty}p^{2}q^{x_{1}}
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    Writing in polar form a complex number

    another way of thinking about this is, what is tangent? sin over cosine. so there needs to be some argument such that sin(x)/cos(x) =√3. So look at the unit circle. what arguments involve the root of 3? π/6 does, but tan of π/6=sin(π/6)/cos(π/6)=1/√3. What else does? π/3. now what do you get?
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    Writing in polar form a complex number

    well, the angle pi/3 gives you √3/2, correct? And you're multiplying on the outside by 2, right? what's cos of the same angle? you're using a different way to make your point. So you need angles to do it in the polar form. If you memorize 3 or 4 pairs from the unit ciricle, I think, you...
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    Determining a confidence interval for data.

    several of my professors have said n=30 is a number that's been around for a while and is used as a rule of thumb, but you don't have to follow it super strictly. How skewed is the data? If it's not horribly skewed, if it's even vaguely bell-shaped, I'd imagine n=20 is acceptable. But please...
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    Finding a marginal pmf

    okay, so my first thought is that the joint then should be \sum_{x_{2}=0}^{\infty}\sum_{i=0}^{x_{2}}p^{2}q^{x_{2}} when I let p=.5, this term does indeed sum to 1, so that's looking alright. oh, I think I maybe figured this out. So I should have (summing over values in the domain...
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    Writing in polar form a complex number

    when i was in complex, the unit circle became my best friend. look at the unit circle, and think about the point that z would make on the unit circle.
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    Finding a marginal pmf

    Homework Statement Suppose that X1 and X2 have the joint pmf f(x_{1},x_{2})=p^{2}q^{x_{2}},x_{1}=0,1,2,...,x_{2},x_{2}=0,1,2,... with 0<p<1,q=1-p Homework Equations The Attempt at a Solution I'm confused because the expression doesn't have x_1 in it. So usually, if I want to...
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    Let Y denote the following subset of . ( )

    okay, so for the first one, can you construct an open ball around any point in A that is contained in A? If you look at Y on a cartesian plane, you have all the points (x,y) where x>0, and y>=0. if you look at A, you have all the points where x>0, and y>0. for every point a=(xo,y0) in A, is...
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    A simple derivative that I can't get for the life of me

    whenever i have a problem like this, i like to move my constants out front and rewrite things in fractions as negative exponents. in your case, i would rewrite the function as ps/(1-qs)=p*(s)(1-qs)^-1. then, ignore the p for now, since you can just multiply it out, and focus on find the...
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    Let Y denote the following subset of . ( )

    i haven't studied topology, but i've studied a little bit of metric spaces. do you use concepts like open balls to show a set is open?
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    Statistics proof regarding integration of cdf

    I'm guessing off your last reply that I'm not in fact allowed to do what I did, and I think I see the reason why: I switched the limits, but not the variables; so I first should have integrated f(t)dx as xf(t), which, evaluated from the proper limits should go to infinity minus negative infinity...
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    Statistics proof regarding integration of cdf

    So I get that I can rewrite F(x+c)-F(x) as ∫xx+cf(x)dx.... is it alright for me to change the order of integration? Because then i would have \intop_{-\infty}^{\infty}\int_{y}^{y+c}f(t)dtdx=\int_{y}^{y+c}\int_{-\infty}^{\infty}f(t)dtdx=\int_{y}^{y+c}1\cdot dx=(y+c)-y=c But I'm not sure if...
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    Statistics proof regarding integration of cdf

    Thank you for your reply. I'm still a bit lost. Is that integral a special form I should recognize? I'm still don't understand how I can say anything about what that equals without knowing what F(x) is. All I know is that it's non-negative and bounded by 0,1. It took me a little while to...
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    Statistics proof regarding integration of cdf

    Homework Statement For any cdf F(x) of a continuous random variable, show that \int_{-\infty}^{\infty}[F(x+b)-F(x+a)]dx=b-a for any a<b. Homework Equations The Attempt at a Solution Not really sure where to begin. I figure I can split the integrals and do u subs, and (after...
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