Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process.

Solution 78E

Step1 of 3:

Let us consider a random variable X it presents thickness measurements of a coating process.

And the thickness measurements are Uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19.

We need to determine the mean and variance of X.

Step2 of 3:

Suppose that a random variable X follows discrete Uniform distribution with parameters [a, b]. Then, the probability mass function of Uniform distribution is given by:

x = 0,1,2,...,n.

We know that mean of Uniform distribution, and it is given by:

Therefore, Mean of X is 0.17 mm.

Step3 of 3:

We know that Variance of Uniform distribution, and it is given by:

Therefore, Variance of X is 0.0068.