Question: hw bonus between end of the bonus hw

```Transcribed text From Image: Write-up on the moment generating function facility for discrete random wribles intended for the course on probability worked on this write-up on Apr 13, 2020/Mon a The moment generating function Search and recall the is a great facility for computing Laplace transform . definition. Andasa the moments of random variables related concept, look not just those that are secrete) up what the charac- in a systematic manner. Let teristic function" as us in this write-up delve into applies to aspin windon variables is all about. how the noment generating - End of Bonus H. function concept applies to Now, now do we make use diserere random variables in of the expectation ineg.1): probability theory, expecially What we do is to compuse for those rondom variables that the derivative of the are particularly of interest tow. LHS in eq. 1 with respect The definition for the moment tot, let us to say generating function of a divirete set t=0. Let ussee random variable X isguren as what this computation follows: brings us to: [exp (X)] = { exp (1 a.) pompy lay E[expex)]/ (09.2) DEL Bonus HW: The moment generating = [explex) finction is known to be related to the Laplace transform of the ==[ Xexpltx Puf (probability mass function). K-pony times and then - 69.200 Scanned with CamScanner
discrete random variablesin of the expectation probability theory, expecially What we do istou for those rendom variables that the derivative of are porticularly of interest to nd. LHS in eg. 1 with The definition for the moment tot, letu lasa- generating function of a discrete K-mory times, and the andom variable xirginen au vet t-o. Letusse what this computa follows a to brings w to: E[exp(+x)]=: 2.00 (tudents leased [ FlexpéXIT, Bonus HW: The moment generating = exp(tX, function is known to be related to the Loplate transform of the puf(probability mass function). Scanned with CamScanner Page of
dom ained not just those that are descrete) up wha in a systematic manner. Let terrutia us in this write-up delve into appliest variables how the moment generating End of a function concept applies to Now, how discrete random variablesin of the expe probability theory, expecially What we do for those rendom variables that the deciran are porticulorly of interest tond. LHS in eg. The definition for the moment tot, letin generating function of a divirece k-many times random variable X isgiren as set to. L what this a follows: E[exp(+X)] =```

`Answer:`