A discrete random variable has probability distribution as shown in the table where    is a finite positive integer.

Show that  .   (3 marks)

Evaluate and in the discrete probability distribution table below, given that  .   (3 marks)

The probability distribution of a discrete random variable, , is given by the table below.

1. Show that  .  (3 marks)
   

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2. Let  .
   
   1. Calculate  .  Answer in exact form.  (2 marks)
      

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   2. Find  .  (1 mark)
      

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The discrete random variable has probability distribution as given in the table. The mean of is 5.

The values of and are