# Hi, does anyone know the what the difference between ux and mx is in the exposed to risk section?

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asked Mar 23, 2016

Are they both calculated as (deaths while x)/(central rate of mortality for age label x) ?

Do they both apply to the same age range?

commented Mar 23, 2016 by (100 points)

The definitions you met in the first part of the course for ux and mx remain the same.

The way these quantities are estimated depend on the underlying assumptions. Note:
• assuming the binomial model ux= (deaths age x)/ (central EXPOSED-TO-RISK age x)
• I expect the applicable age ranges for ux and mx to differ with mx applying to ages at the start of the rate interval and ux, age at middle of rate interval (assuming UDD).

$$\mu x$$ is a force of mortality. It is a rate.
$$mx$$ is a weighted average of this force, weighted by population. If the size of the population is larger, $$\mu x$$ has a larger population on which to act. As the population decreases from the resulting deaths, $$\mu x$$ has a smaller population on which to act.
These two measure are equivalent if $$\mu x$$ is constant for age label $$x$$. In the estimation procedure, this is assumed and as such the estimations are the same.