Introduction to Probability Theory

Computer Lab 3: More on Random Variables

Solve the word problems below and use the computer to check your answers either by simulation with the Calc -> Random Data and/or with the Calc -> Probability Distributions function.

1. (From A First Course in Probability by Sheldon Ross, Prentice Hall, 2002) Two balls are chosen randomly from an urn containing 8 white, 4 black and 2 orange balls. Suppose that we win $2 for each black ball selected and we lose $1 for each white ball selected. Let X denote our winnings. What are the possible values of X and what are the probabilities associated with each value?

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

2. (From A First Course in Probability by Sheldon Ross, Prentice Hall, 2002) Two fair dice are rolled. Let X equal the product of the 2 dice. Compute Pr (X = i) for i = 1, 2, ...

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

3. (From A First Course in Probability by Sheldon Ross, Prentice Hall, 2002) Let X represent the difference between the number of heads and the number of tails when a coin is tossed 3 times. What are the possible values of X and what are the corresponding probabilities?

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

4. (From An Introduction to Mathematical Statistics and its Applications by R.J. Larsen & M.L. Marx, Prentice Hall, 2001) An urn contains five chips, numbered 1 through 5. Two are drawn without replacement. Tabulate the probability function for X, the larger of the two.

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

   
   

5. (From An Introduction to Mathematical Statistics and its Applications by R.J. Larsen & M.L. Marx, Prentice Hall, 2001) An urn contains four chips, numbered 1 through 4, where the probability associated with a chip is proportional to its magnitude. Find and graph the distribution function corresponding to the number showing on the chip drawn at random.