Distribution of drops

xog

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On a terrace , it has rained. The terrace is covered with 100 square-shaped tiles, each 50 cm x 50 cm. In total, 1000 raindrops have fallen on the terrace. You then count the raindrops that have fallen on each tile. Considering the tiles individually, what is the expected distribution of the number of drops? How many tiles do you expect to have received 0, 1, 2, 3, ... drops?
 
With the information given the distribution for a single drop hitting a given tile will be discrete uniform.
The probability a drop will hit a given tile is constant with p=1/100.

That then generates a binomial distribution on the number of drops out of 1000 hit a given tile.
I leave you to work out the distribution parameters and the final expression and expectations.
 
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so is the expected distribution 10 (because 1000/100=10)
and is f(0)=(99/100)^1000
then f(1)=99!/100^99
and f(n)=(f(1))^n
because I am not sure if the solution is right
 
For each tile \(\displaystyle P[\text{hit by k drops}]= \dbinom{1000}{k}p^k(1-p)^{1000-k},~\text{where }p=\dfrac{1}{1000}\)

Now try working out the expectations of how many tiles receive \(\displaystyle k\) drops.
 
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For each tile \(\displaystyle P[\text{hit by k drops}]= \dbinom{1000}{k}p^k(1-p)^{1000-k},~\text{where }p=\dfrac{1}{1000}\)

Now try working out the expectations of how many tiles receive \(\displaystyle k\) drops.

my bad \(\displaystyle p=\dfrac{1}{100}\)
 
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