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  • m.g.f?

    I was wondering how you would do these problems here:.

    Let X be a random variable with m.g.f. given by
    Find the following: M(t)=(.3+.7e^t)^5

    a. The name of the distribution, with appropriate parameters.
    b. The mean and variance of X.
    c. P(1 ≤ X ≤ 2)

    A random variable X has m.g.f. given by


    a. The mean and variance of X.
    b. P(X ≥ 1)


    If X has a Poisson distribution so that 3P(X = 1) = P(X = 2), find P(X = 4)

    Don't worry, I didn't post this in 3 forums like last time.
    Thanks for your help.

  • #2
    To find the mean and variance of x do I just take the 1st and 2nd derivatives of the function?
    And also for P(x greater than or equal to 1), do I go 1-P(x less than one) and go 1-integral from 0 to 1 of the function?
    How about the rest of these problems?


    • #3
      Mean is the E(X) or first moment. Take the first derivative of the moment generating function and set t = 0. Variance is E(X^2)-E(X)^2 or the second moment (second derivative, set t=0) minus the square of the mean.


      • #4
        I understand MGF's can be a confusing topic. It took me a while as well to become comfortable with them. My problem with this thread concerns your third question. With all due respect, plugging in numbers and solving for the Poisson distribution should be trivial at this point. This really makes me think that you're getting us to do your homework for you.


        • #5
          Yeah - getting the hang of mgfs can be difficult, but it's not so hard once you get used to it - I recommend just practicing the examples a few times until it's second nature.

          I actually have my second probability exam (in college) a week from tomorrow, and while I still need to practice a bit, I'm rather confident. My only non-A so far this semester was the first exam, due to some -really- stupid mistakes (there are NOT 13 aces in a deck ).