How to find the mean of percentages
1 answer:
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a) Probability of both being males is 27%
b) Probability of both being females is 23%
c) Probability of having exactly one male and one female is 50%
Step-by-step explanation:
a)
The probability that the birth is a male can be written as
(which corresponds to 52%)
While the probability that the birth is a female can be written as
(which corresponds to 48%)
Here we want to calculate the probability that over 2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:
And substituting, we find
So, 27%.
b)
In this case, we want to find the probability that both children are female, so the probability
As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:
And substituting
We find:
Which means 23%.
c)
In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:
- The probability that 1st child is a male and 2nd child is a female, namely
- The probability that 1st child is a female and 2nd child is a male, namely
So, this probability is
We have:
Therefore, this probability is
So, 50%.
Learn more about probabilities:
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Answer:
See explanation below.
Step-by-step explanation:
When we want to fit a linear model given by:
Where y is a vector with the observations of the dependent variable, the parameters of the model and x the vector with the observations of the independent variable.
For this case this population regression function represent the conditional mean of the variable Y with values of X constant. And since is a population regression the parameters are not known, for this reason we use the sample data to obtain the sample regression in order to estimate the parameters of interest
We can use any method in order to estimate the parameters for example least squares minimizing the difference between the fitted and the real observations for the dependenet variable. After we find the estimators for the regression model then we have a model with the estimated parameters like this one:
With
And this model represent the sample regression function, and this equation shows to use the estimated relation between the dependent and the independent variable.