Solution Found!
The thickness Xof a wooden shim (in mm) has probability
Chapter 2, Problem 16E(choose chapter or problem)
The thickness of a wooden shim (in
) has probability density function
\(f(x)=\left\{\begin{array}{cc}
\frac{3}{4}-\frac{3(x-5)^{2}}{4} & 4 \leq x \leq 6 \\
0 & \text { otherwise }
\end{array}\right.
\)
a. Find \(\mu_X\).
b. Find \(\sigma_X^2\).
c. Let denote the thickness of a shim in inches (1 mm = 0.0394inches). 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.
Equation Transcription:
Text Transcription:
f(x)={_0 otherwise^{3 over 4}-{3(x-5)^2 over 4} 4{</=}x{</=}6
mu_X
sigma_X^2
(1 mm=0.0394 inches)
mu_Y
sigma_Y^2
Questions & Answers
QUESTION:
The thickness of a wooden shim (in
) has probability density function
\(f(x)=\left\{\begin{array}{cc}
\frac{3}{4}-\frac{3(x-5)^{2}}{4} & 4 \leq x \leq 6 \\
0 & \text { otherwise }
\end{array}\right.
\)
a. Find \(\mu_X\).
b. Find \(\sigma_X^2\).
c. Let denote the thickness of a shim in inches (1 mm = 0.0394inches). 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.
Equation Transcription:
Text Transcription:
f(x)={_0 otherwise^{3 over 4}-{3(x-5)^2 over 4} 4{</=}x{</=}6
mu_X
sigma_X^2
(1 mm=0.0394 inches)
mu_Y
sigma_Y^2
ANSWER:
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.