# Probability

Compute š(š) for the following random variable š:
š=Number of tosses until getting 4 (including the last toss) by tossing a fair 10-sided die.

š(š)=

Compute š(š) for the following random variable š:
š=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 š(š) be the expected number of additional tosses until all 10 numbers are seen (including the last toss) given š distinct numbers have already been seen.

Find š(10).

š(10)=

Write down a relation between š(š) and š(š+1). Answer by finding the function š(š) in the formula below.

For š=0,1,ā¦,9:
š(š)=š(š+1)+š(š)

where š(š)=

Finally, using the results above, find š[š].

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

š[š]=

Ty a lot

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1. E[10]= 10

10/(10-i)

29.29

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2. @juanpro - E[10] =10 - I am pretty confused.
Can you please explain how it is 10?

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3. E(10) Must be 0. All Other Answers are Right though.

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4. š=Number of tosses until getting 4 (including the last toss) by tossing a fair 10-sided die.
š(š)=
whats the answer of this

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5. Please explain this further

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6. E(10)=0

The induction step is as follows. For i=1,ā¦9:
E(i) = (E(i)+1)Ći10+(E(i+1)+1)Ć(1āi10)
āŗ E(i) = E(i+1)+1010āi.

Using E(10)=0 and the induction step, we have
E(0) = 1010+109+ā¦+102+101+0ā29.28968.

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7. 2) 10/(10-i)
sorry for the typo

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