Dr Harris has recently received the following gifts:  one partridge, two turtle doves, and three French hens.  Unfortunately, she does not have space for all six birds so she selects two at random to keep.   Let ?R be the random variable counting the number of partridges kept, and ?T be the random variable counting the number of turtle doves kept. (i) Determine the joint probability mass function of the random variables ?R and ?T, and write it in the form of a table with six entries.  (ii) Explain briefly how you could check your answer to (i).  (iii)  State the name for the distribution of ?R, and specify any parameters.

Dr Harris has recently received the following gifts:  one partridge, two turtle doves, and three French hens.  Unfortunately, she does not have space for all six birds so she selects two at random to keep. 

 Let ?R be the random variable counting the number of partridges kept, and ?T be the random variable counting the number of turtle doves kept.

(i) Determine the joint probability mass function of the random variables ?R and ?T, and write it in the form of a table with six entries. 

(ii) Explain briefly how you could check your answer to (i). 

(iii)  State the name for the distribution of ?R, and specify any parameters.