Question

Compute E(X) for the following random variable X : X=Number of tosses until all 10 numbers are seen (including the last toss) by tossing a fair 10-sided die. To answer this, we will use induction and follow the steps below: Let E(i) be the expected number of additional tosses until all 10 numbers are seen (including the last toss) given i distinct numbers have already been seen. Find E(10) . E(10)=

Answer 1

Answer:

For 10 tosses we have that E(X)=10

Therefore E(i)= 1/10 +2/10 +3/10....10/10

This implies that 40/10=E(i)

Therefore E(10) =40/10

= 4.