Suppose that a child desires 10 different toys for her birthday. Twenty people will come to her birthday party, each of them equally likely to bring any one of the 10 toys. Let X be the number of different types of toys brought to the party. Note that X can be any integer from 1 to 10. What is E[X]? Justify your answer.

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Respuesta :

saifsofia saifsofia · Answer 1 · 2019-12-14T19:55:09+01:00

Answer:

8.784

Step-by-step explanation:

There are 10 different toys, hence let

i = 1, 2, .... 10

The expected value for each different toys is debited such that E(Xi). For example, the expected value for the first toy is E(X1)

Since 10 toys, so we have E(X1), E(X2),..(E(X10)

Total expectation value E(X) will be

E(X) = E(X1) + E(X2) +..(E(X10)

Then, to make it simpler, we set the condition of the probability by setting the value of getting a toy to be 1 and not getting a toy to be 0

Also note that the number of people coming to the party is 20 and they are equally likely to bring any one of the 10 toys.

Therefore,

E(Xi) = P(Xi=1) = 1 - (9/10)^20

So for total expectation value,

E(X) = E(X1) + E(X2) +..(E(X10)

= 10*(1 - (9/10)^20)

= 8.784