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Moment generating function

Could someone help me out with this question?

X= 1/2......prob. 1/2
-1/2..... prob. 1/2

It asks to find the first four moments about the origin. I just don’t get the correct answers (0, 1, 0, 1)
Original post by Andy Lau
Could someone help me out with this question?

X= 1/2......prob. 1/2
-1/2..... prob. 1/2

It asks to find the first four moments about the origin. I just don’t get the correct answers (0, 1, 0, 1)


What do you get and how do you get it? I hope it's at least intuitively clear that the first and third moments are zero...
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Andy Lau
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Original post by Gregorius
What do you get and how do you get it? I hope it's at least intuitively clear that the first and third moments are zero...


I firstly worked out the mgf (e^t/2+ e^-t/2)/2, which is cosh t/2. Expand this i got 1/4 for the second and 1/16 for the fourth.....not correct.
Original post by Andy Lau
I firstly worked out the mgf (e^t/2+ e^-t/2)/2, which is cosh t/2. Expand this i got 1/4 for the second and 1/16 for the fourth.....not correct.


Looks to me that you're correct.

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