Solution Found!
The thickness X of a wooden shim (in mm) has probability density function f (x) = 3 4
Chapter 2, Problem 16(choose chapter or problem)
The thickness X of a wooden shim (in mm) has probability density function
\(f(x)= \begin{cases}\frac{2}{4}-\frac{3(x-5)^{2}}{4} & 4 \leq x \leq 6 \\ 0 & \text { otherwise }\end{cases}\)
a. Find \(\mu_{X}\).
b. Find \(\sigma_{X}^{2}\).
c. Let Y denote the thickness of a shim in inches \((1 \mathrm{\ mm}=0.0394 \text { inches })\). Find \(\mu_{Y}\) and \(\sigma_{Y}^{2}\).
d. If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.
Questions & Answers
QUESTION:
The thickness X of a wooden shim (in mm) has probability density function
\(f(x)= \begin{cases}\frac{2}{4}-\frac{3(x-5)^{2}}{4} & 4 \leq x \leq 6 \\ 0 & \text { otherwise }\end{cases}\)
a. Find \(\mu_{X}\).
b. Find \(\sigma_{X}^{2}\).
c. Let Y denote the thickness of a shim in inches \((1 \mathrm{\ mm}=0.0394 \text { inches })\). Find \(\mu_{Y}\) and \(\sigma_{Y}^{2}\).
d. If three shims are selected independently and stacked one atop another, find the mean and variance of the total thickness.
ANSWER:Step 1 of 6
A probability density function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It is a non-negative function that integrates to 1 over the entire range of the random variable. This means that the area under the PDF curve between any two points represents the probability that the random variable will take on a value within that range.