Question

Compare the method of calculating expected value with the table of values to the formula for Binomial Distribution. What are the pros and cons of each.

Answer 1

In using table of values we use jotted down probabilities to calculate the expectations, while using the formula for binomial distribution, we explicity calculate these probabilities using the formula for the pmf. Both have their advantages and disadvantages.

For the table method the calculations are really easy with small values of n (as we get rid of a lot of calculations. We just need to perform some summations on a calculator.) On the other hand, tables are not flexible as you won't get probabilities for very large values of n.

The formula method is tiresome as we have to compute the probabilities by hand and then carry out the summation. On the other hand it is flexible, as we can (ideally) compute the probabilities for any values of n. Also computing softwares are more compatible with mathematical formulae than jotted down probabilities.