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

    1. 👍 4
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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)Ɨi10+(E(i+1)+1)Ɨ(1āˆ’i10)
    āŸŗ E(i) = E(i+1)+1010āˆ’i.

    Using E(10)=0 and the induction step, we have
    E(0) = 1010+109+ā€¦+102+101+0ā‰ˆ29.28968.

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

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