Question

A certain part consists of a lamina of two layers of the same material. Layers have...

A certain part consists of a lamina of two layers of the same material. Layers have thicknesses that are normally distributed with a mean of 1.2mm with a standard deviation of 0.02mm. These two thicknesses are correlated with p=0.4.

What is the distribution of the total thickness?

Math   Statistics-And-Probability   
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Answer #1

Let T shows the total thickness. Let X is a random variable shows the thickness of layer 1 and Y is a random variable shows the thickness to layer 2. So we have

T = X+Y

And

Since X and Y are normally distributed so T will also have normal distribution with mean and SD as follow

That is  distribution of the total thickness will be normal distribution with mean 2.4 and standard deviation 0.0335.

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