# Thread: Question on joint pdf and normal distribution

1. ## Question on joint pdf and normal distribution

At one stage in the manufacture of an engine a piston of circular cross-section has to fit into a similarly-shaped cylinder. The distributions of diameters of pistons and cylinders are known to be normal with parameters:

• Piston diameters: mean 10.42cm, standard deviation 0.03cm.
• Cylinder diameters: mean 10.52cm, standard deviation 0.04cm.

(a) What is the probability that in 100 pairs, selected independently and at random, every piston will fit?

Any help would be greatly appreciated

2. ## Re: Question on joint pdf and normal distribution

Hey sakuraxkisu.

For these kinds of problems you need to think about the distribution.

We know that for independent variables the distribution of P(A and B) = P(A)P(B): In this case A corresponds to one piston fitting and B corresponds to another piston fitting.

So if you find the probability of one piston fitting, then as long as every piston has the same distribution, you can raise this probability to the power of 100 to get the final probability that every single piston fits.

Its just based on the inductive definition of independence where the three variable case is P(A and B and C) = P(A)P(B)P(C)