The table contains a hospital's probability distribution chart of the number of babies born per day for a week. Determine the mi
ssing probability in the distribution, and then answer this question: What percentage of time should a sufficient number of nurses be on duty to care for at least seven babies?
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Answer:
Step-by-step explanation:
The main idea is that I would like to pay less than what I'm expecting to win, so in that way, I get a profit out of playing this game. Let X be the number of tosses until I get a Heads. By definition, this is a geometric random variable with parameter p = 1/2.
Let Y the amount I received for playing. So, we want to calculate the expected value of Y.
We can calculate it as follows
Since X is a geometric random variable, we have that
Then,
So, we expect to have an infinite amount. Given this, we can pay as much as we want to play the game.