The thickness Xof a wooden shim (in mm) has probability density function

a. Find μX

b. Find

c. Let Y denote the thickness of a shim in inches (1 mm = 0.0394 inches). Find μγ and

d. If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.

Solution 16E

Step1 of 5:

We have a random variable X it presents the thickness of wooden shim and it has a probability density function:

Here Our goal is:

a).We need to find

b).We need to find

c).We need to Find and by taking Y as the thickness of a shim in inches (1 mm = 0.0394 inches).

d). If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.

Step2 of 5:

a).

=

=

= [therefore ]

=

=

=

=

= -27 - (-32)

= -27 + 32

= 5

Hence, = 5.

Step3 of 5:

b).

=

=

= [therefore ]

=

=...