moment pgf question

[galbax02]

Let Mx(t) be the moment pgf for the random variable X and define S(t) = ln Mx(t). Show that:

 

[Deleted member 4993]

Let Mx(t) be the moment pgf for the random variable X and define S(t) = ln Mx(t). Show that:
View attachment 24708

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[galbax02]

I have a huge list of problems, I posted 5 on the forum but I have no idea on how to start and develop them, I need help in the entire exercise. I read the rules.

 

[Deleted member 4993]

Let Mx(t) be the moment pgf for the random variable X and define S(t) = ln Mx(t). Show that:
View attachment 24708

Can you provide the definitions of:

• pgf (probability generating function)
  
  
• Moment of pgf (probability generating function)
  
  
• E(X)
  
  
• Var(X)