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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)=

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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.

The probability of getting E(10) will be 29.29.

How to calculate the probability?

From the information given, the probability of getting 4 by tossing a fair 10 sided die will be 1/10.

E(X) = 1/p = 1/0.1 = 10

Therefore, E(10) will be calculated thus:

= 10/(10 - 9) + (10/10 - 8) + 10/(10-7) ....

= 10 + 5 + 3.33 + 2.5 + 2 + 1.67 + 1.43 + 1.25 + 1.11 + 1

= 29.29

Learn more about probability on:

https://brainly.com/question/24756209

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