Solution Found!
Let the distribution function of a random variable Y be a
Chapter 4, Problem 19E(choose chapter or problem)
Let the distribution function of a random variable be
\(F(y)=\left\{\begin{array}{ll}
0, & y \leq 0, \\
\frac{y}{8}, & 0<y<2, \\
\frac{y^{2}}{16}, & 2 \leq y<4, \\
1, & y \geq 4 .
\end{array}\right.
\)
a Find the density function of .
b Find \(P(1 \leq Y \leq 3)\).
c Find \(P(Y \geq 1.5)\).
d Find \(P(Y \geq 1 \mid Y \leq 3)\).
Equation Transcription:
Text Transcription:
F(y)=
0, y</=0,
u over 8, 0<y<2,
y^2 over 16, 2</=y<4,
1, y>/=4.
P(1</=Y</=3)
P(Y>/=1.5)
P(Y>/=1|Y</=3)
Questions & Answers
QUESTION:
Let the distribution function of a random variable be
\(F(y)=\left\{\begin{array}{ll}
0, & y \leq 0, \\
\frac{y}{8}, & 0<y<2, \\
\frac{y^{2}}{16}, & 2 \leq y<4, \\
1, & y \geq 4 .
\end{array}\right.
\)
a Find the density function of .
b Find \(P(1 \leq Y \leq 3)\).
c Find \(P(Y \geq 1.5)\).
d Find \(P(Y \geq 1 \mid Y \leq 3)\).
Equation Transcription:
Text Transcription:
F(y)=
0, y</=0,
u over 8, 0<y<2,
y^2 over 16, 2</=y<4,
1, y>/=4.
P(1</=Y</=3)
P(Y>/=1.5)
P(Y>/=1|Y</=3)
ANSWER:
Solution
Step 1 of 4
a) From the given function we have to find density function
Given
=
=
=
To get the density function we have to differentiate the given function with respect to ‘y’
Then
=
=
=