Name(s):                                                           :
Break the Ice Problems for
Moment Generating Function Combinations
Tom Linton, February 28, 2000
  1. Let X be Normal(10, 3) (i.e. with a mean of 10 and standard deviation of 3).
    1. Find the moment generating function for Y = 5X.

      2.  

       





       
       
       
       

    2. What type of random variable (give both the flavor and the values of the parameters) is Y?






      3.  
       

  2. Let X be an exponential random variable with beta = 4. Let Y = 2X.
    1. Find the moment generating function for Y.

      2.  

       
       
       





       
       

    2. What type of random variable is Y?

      3.  

       





       

  3. Let X and Y be independent random variables, both exponential with beta = 4.
    1. Find the moment generating function of U = X + Y.

      2.  

       
       
       
       
       
       
       
       

    2. What type of random variable is U?

      3.  

       
       
       
       
       
       

  4. Can you explain why the answers to part (b) of questions 2 and 3 are different? Think about the differences between:
    5. If this doesn't clarify things, think about calculating P[2X < 6] versus calculating P[X + Y < 6].