Question

If 30 tickets are numbered consecutively from 1 to 30, and 2 tickets aré selected at random without replacement, find expected (sum of the numbers on the two tickets) and find the variance (sum of the numbers on the two tickets).

Step 1

let X be the sum of numbers. X can range from 3 to 59.

Make the 30 by 30 grid for ease of calculations where at the intersection of any two numbers lies their sum.

It is impossible to fit the entire worksheet here but i've written formulae and displayed Excel functions so that you can do this easily. I have also included answer screen so that you can verify your answers.

Step 2

Don't be intimidated by the table. After you fill in the first 2 lines, just drag. Make sure you use the dollar signs wherever required. Notice how 1,1 or 2,2 or 3,3 are all zero. That is because we are drawing without replacement so any two tickets that are drawn will be different from each other..

Step 3

Now we know that sum can range from 3 to 59 , let's count how many occurences of each sum are which in turn will help us calculate ...

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