# What's the probability that all three parts would fail within 2 years of each other? (joint PDF)

Suppose an instrument has three independent parts, all of whose lifetimes (in years) are modeled by an exponential pdf which is $$f_Y(y)=e^{-y}, y>0.$$ What's the probability that all three parts would fail within two years of one another?

I understand how to find the cdf, and also now know a different way to solve this. But I'm wondering, is it possible to solve this using the formula for joint PDFs of order statistics? If so, how? I'm having trouble seeing if/how this formula can be used.

This is the formula: $$f^{'}_{Y_i,Y_j}(u,v)=\frac{n!}{(i-1)!(j-i-1)!(n-j)!}[F_Y(u)]^{i-1}[F_Y(v)-F_Y(u)]^{j-i-1}[1-F_Y(v)]^{n-j}f_Y(u)f_Y(v)$$ for $$i < j$$ and $$u

Thank you!