Gentle introduction to moment generating functions

Описание: 0:13 What are moments in statistics? (centered, uncentered)
1:57 What is the mgf? The useful properties of the mgf is when it exists in the neighbourhood of 0, so we state it in the definition. Some sources do not have this requirement in their definition.
3:05 Computing moments ( example for discrete random variable)
5:16 Easy to forget to check mgf exists for t around zero. In the example, the mgf exists for all real t, so yes, mgf exists for t around zero.
9:40 Distribution of a sum of independent random variables
10:30 Distribution of a linear function of independent random variables (example)
13:47 Comments
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Mgfs - standard continuous r.v
Exponential distribution
   • #56 Moment generating function of the expo...  
   • #57 Moment generating function of the expo...  
Standard normal
   • #62 Moment generating function of the stan...  
   • #63 Moment generating function of the stan...  
Continuous uniform
   • #60 Moment generating function of the cont...  
   • #61 Moment generating function of continuo...  

Mgfs - discrete r.v
Binomial
   • #50 Moment generating function of the bino...  
   • #51 Moment generating function of the bino...  
Poisson
   • #67 Moment generating function of Poisson-...  
   • #68 Moment generating function of Poisson ...  
Geometric
   • #53 Moment generating function of geometri...  
   • #54 Moment generating function of geometri...  
Negative binomial
   • #48 Moment generation function of the nega...