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Suppose E(X|Y) and that a figure illustrates expected salary as a function of gender and that it shows that the mean for women is $2500 \$$ and for men is $3500\$$. If $50\%$ are women and $50\%$ men, the variance is 250 000. How to get there, how to calculate the variance and plot the figure?

It is the variance in the means that are meant here.

ASKING
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  • This is not clear. First of all, the units for variance should not be "dollars" here. Secondly, there's nothing to calculate. We are given the variance. We have no information regarding the variance other than that raw value. – lulu Feb 28 '20 at 14:41
  • I edited the units of variance. – ASKING Feb 28 '20 at 14:48
  • But the second part of my comment was more important. We have no information about the variance other than the raw value, which was handed to us. There is nothing to calculate. – lulu Feb 28 '20 at 14:49
  • Do you have any hypothesis about the genders' relative variances, e.g. that they're equal, or proportional to some power of the gender means? – J.G. Feb 28 '20 at 14:57
  • If you have the raw data (everybody's salary) then there is no difficulty calculating the variance, just from the definition. – lulu Feb 28 '20 at 15:09
  • I added to the body of the post a question; how to plot the figure? – ASKING Feb 29 '20 at 14:26

1 Answers1

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The random variable being discussed is a sample mean, conditioned over gender.

The mean of this sample mean is $(2500+3500)/2$ which is $3000$.

$$\mathsf E(\bar X)=\sum_x x\, \mathsf P(\bar X{=}x)$$

The variance of the sample mean is $((2500-3000)^2+(3500-3000)^2)/2$ which is $250\,000$.

$$\mathsf{Var}(\bar X)=\sum_x (x-\mathsf E(\bar X))^2\,\mathsf P(\bar X{=}x)$$

Graham Kemp
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