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msjsnell29
07.03.2020 •
Mathematics
Suppose you have a bag of 10 coins. Nine of them are fair coins, that is, if you toss any of these 9 coins the probability of getting a head, P(H) = 1/2. Similarly, probability of getting a tail, P(T) = 1/2. The other coin is biased — it has head on both sides. Use indicator random variables to compute expected number of heads, if all 10 coins are tossed together.
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Ответ:
Step-by-step explanation:
Given:
we have 10 coins
nine of them are fair coins, which means:![P(H)=\frac{1}{2}; P(T)=\frac{1}{2}](/tpl/images/0538/0566/b7e79.png)
but one coin is biased it has head on both sides which means![P(H)=\frac{1}{1}; P(T)=\frac{0}{1}=0](/tpl/images/0538/0566/d4fb4.png)
expected number of heads for tossing 9 coins =![9(\frac{1}{2})=\frac{9}{2}=4.5](/tpl/images/0538/0566/f99a7.png)
The coin 10 is biased with only head on both sides
The expected number of heads tossing this coin is = 1
Therefore, the expected number of heads if all 10 coins are tossed together is =![4.5+1=5.5](/tpl/images/0538/0566/198ae.png)
Using indicator random variables:
The number of unbiased coins = 9: n=9
One coin is biased with only head. Therefore:
Finally,![F(x)=4.5+1=5.5](/tpl/images/0538/0566/4acfd.png)
The expected number of heads = 5.5
Ответ:
The constant speed of Fast freddy is 1/4
The constant speed of Speedy Sam 1/8
Fast Freddy ran faster
Step-by-step explanation:
Edgenuity