Question

A fair die is rolled repeatedly. Find the expected number of rolls until all 6 faces appear.

Answer 1

Answer:

• The time until the point when the principal result shows up is 1 after that the arbitrary time until a second (unique) result shows up is geometrically dispersed with parameters of accomplishment 5/6,hence with mean 6/5(recall that the mean of a geometrically disseminated irregular variable is the reverse of its parameters).
• After that,the irregular time until a third (different)result shows up is geometrically circulated with parameters of achievement 4/6,hence with mean 6/4.And so on,until the irregular time of appearance of the last and 6th result,which is geometrically appropriated with parameters of progress 1/6,hence with mean 6/1 this demonstrates the mean aggregate time to get every one of the six outcomes is

6/k=147/10

=14.7