Recent content by mathmajor23

  1. M

    Multivariable Probability Distribution

    Thanks a bunch! I, too, hate the annoying indicator functions, but my professor seems the need to "require" us to use them.
  2. M

    Multivariable Probability Distribution

    Ok, hopefully here's the final check: fx(x) = ∫ from x to infinity [2e^(-x-y)]dy =-2[e^(-x-y)] from y=x to y=∞ = 2e^(-2x) I[0,∞) (x) fy(y) = 2[e^(-y)-e^(-2y)] I [0,infinity) (y) f(x|y) = 2e^(-x-y) / 2[e^(-y)-e^(-2y)] = [e^(-x)] / (1-e^(-y)) I[0,∞) (x) f(y|x) = 2e^(-x-y) /...
  3. M

    Multivariable Probability Distribution

    Let's start over. I originally had for the marginal of X: ∫ from 0 to x of [2e^(-x-y)]dy =-2[e^(-x-y)], evaluated from y=0 to y=x = 2[e^(-x)-e^(-2x)] I[0,∞) (x) To check this, I integrated this and it came out to 1, so I'm not sure why this is wrong.
  4. M

    Multivariable Probability Distribution

    Which part of f(x) = 2[e^(-x)-e^(-2x)] I [0,infinity) (x) is wrong?
  5. M

    Multivariable Probability Distribution

    Was my conditional of f(x|y) correct? Hmm is this the MD of x then? Integral from 0 to infinity [2e^(-x-y)dy] = -2(e^(-x-y)] from y=0 to y=infinity =2[1+e^(x)] I [0,infinity) (x)
  6. M

    Multivariable Probability Distribution

    I got that k=2, and checked it by seeing it integrated to 1. For the Marginal Distributions of X and Y, I got : f(x) = 2[e^(-x)-e^(-2x)] I [0,infinity) (x) f(y) = 2[e^(-y)-e^(-2y)] I [0,infinity) (y) Then, for the conditionals, I got: f(x|y) = e^(-x) / [1-e^(-y)] I[0,infinity) (x)...
  7. M

    Multivariable Probability Distribution

    What's the integral of the inner part evaluate to? I tried using integration by substitution but it's not working.
  8. M

    Multivariable Probability Distribution

    Oops! So it should be ∫from 0 to ∞ ∫ from 0 to x [f(x,y)dxdy] ?
  9. M

    Multivariable Probability Distribution

    Yes, it's the same as single variable. I'm just unsure on my bounds of my integrals.
  10. M

    Multivariable Probability Distribution

    f(x,y) = ke^(-x-y), 0<x<∞ , 0<y<∞ , and x<y Find k to make this a PDF. So I set up: ∫(from 0 to ∞)∫(from 0 to ∞) [ke^(-x-y)]dxdy. Is this integral right? I also need to find the marginals of X and Y but my k has to be right first.
  11. M

    Finding if a Series is Convergent

    If you're getting ∞ as an answer, then the series diverges, not converges.
  12. M

    Order Statistics Probabilities

    FX(1)(x) = P(X(1) <= x) = P(X1,...,Xn <= X) =1-P(X1,...,Xn > X) =1-P(X1>X)^n since the xi's are iid. =1-[1-P(X1 <= X)]^n =1-[1-F(x)]^n =1-[1-∫ from 0 to x (2tdt)]^n =1-(1-X^2)^n For the probability, P(X1>.2) = 1-Fx(1) (0.2) = (1-(0.2)^2)^n = (0.96)^n
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    Probability - Conditional Expectation

    P(A|A+B=c) = P(A|B=c-A) = P(A and B=c-A) / P(B=c-A) =P(α + β) / P(β) ?
  14. M

    Conditional Probability for discrete random variables.

    I'm also trying to solve this similar problem, and also have no idea how to go about solving it.
  15. M

    Probability - Conditional Expectation

    Can anyone show me this problem step by step? I'm not picking up on any of this question, which is why I posted this.
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