If you’re pregnant, theprobability of having a boy or girlis the same: 50%. However, if you already have one child (say, a boy), your odds change. Given that your first child is a boy, your odds of having another boy drop to one third (33.33%). The reason for th...
If you look at it from the point of view of expectation things are simpler.The probability of having a boy first is 1/2, at which point the family stops and you have a ratio of 1 boy per 1 births. The probability of having one girl, then one boy is 1/4, at which point you ...
In Example 23.2.1 the overall probability of a particular value of a discrete random variable was computed as a product in which one factor was the number of equally likely ways in which that value could be obtained, and the other factor was the probability of each mutually exclusive occurrenc...
If you assume that the prior probability of a child being a boy is 1/2, then the probability that she has two boys, on the information given, is 1/3. The prior probabilities were: 1/4 two boys, 1/2 one boy one girl, 1/4 two girls. The mathematician's "Yes" response has proba...
A benefit of having optimized team parameter values is that it allows us to make comparisons and predictions across any two teams even if these teams have not played each other and even if these teams do not have any common opponents. The optimization process is robust enough to evaluate every...
In summary, the problem is asking for the probability of a family having a girl when there is at least one boy, which is equivalent to the probability of two randomly chosen children being of different genders, excluding the case of two girls. The answer is 2/3, as...
More broadly,the existence of causal relationships does not dependin any wayon our ability to understand or describe (model) them, or on whether we happen to have an existing scientific framework to fit them in. I used to see this kind of insistence on having a known mechanism as adumb ...
Recently someone asked me to explain how to solve a couple of problems which went like this: "Find the expected time before XYZ happens". Note that here the time to completion is a random variable, and in probability theory, such random variables are called "stopping times" for obvious reas...
I used to see this kind of insistence on having a known mechanism as a dumb argument made by smart people, but I’m coming to see it in a much darker light. The more I learn about the history of science, the more clear it becomes that the primary impediment to the ...
The interviewer is looking for two things: the ability to think probabilistically, and evidence of having studied stochastic processes. "Elementary Probability Theory" by Kai Lai Chung "Probability and Random Processes" by Geoffrey Grimmett and David Stirzaker ...