1)Compute()

for the following random variable

:

=Number of tosses until getting 4 (including the last toss) by tossing a fair 10-sided die.

()=?

2) Compute()

for the following random variable

:

=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()

be the expected number of additional tosses until all 10 numbers are seen (including the last toss)given

distinct numbers have already been seen.

1. Find(10) = (0??? my guess)

Write down a relation between()

and(+1)

. Answer by finding the function()

in the formula below.

For=0,1,...,9

:

()=(+1)+()

where()= [my guess = (10/10-i)

Finally, using the results above, find[]

.

(Enter an answer accurate to at least 1 decimal place.)

[] =??