Expected value in a triangular distribution

Hi All,

I'm struggling to understand following problem. It says,
Demand follows a triangular distribution.
Minimum 500
Mode 6,000
Maximum 24,000
Expected demand is given as 10,167. To me, expected value should be the mode i.e. 6000.
I'm struggling to understand the reasoning.

I shall be highly obliged if anyone can explain this to me.



TS Contributor
If you think that mode is always equal to the expected value, then it means that you have not learn the definition of them properly and mixed them up.

By definition for a continuous random variable \( X \), the mode is the maximum point of its pdf \( f_X \)

and the expected value is the integral \( \int_{-\infty}^{+\infty} xf_X(x)dx \)

Therefore they are completely different concepts. Maybe you only have some nice distributions, like normal distribution which is symmetric and unimodal in your mind which in turns make you think that all distributions are like that.