Please your support with this Expectations Excercise:

ComputeE(X) for the following random variableX :

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:

LetE(i) be the expected number of additional tosses until all 10 numbers are seen (including the last toss)giveni distinct numbers have already been seen.

1. FindE(10)
2. Write down a relation betweenE(i) andE(i+1) . Answer by finding the functionf(i) in the formula below. Fori=0,1,...,9 E(i)=E(i+1)+f(i)wheref(i)= ?
3. Finally, using the results above, findE[X] (Enter an answer accurate to at least 1 decimal place.) E[X]= ?