Given
Uniform distribution
a = 1
b = 9
Procedure
B) Graph the probability distribution
C)Find the probability density function p(x)=
[tex]\begin{gathered} p(x)=\frac{1}{b-a} \\ p(x)=\frac{1}{8} \\ p(x)=0.125 \end{gathered}[/tex]
D)Find the mean
[tex]\begin{gathered} \mu=\frac{a+b}{2} \\ \mu=\frac{9+1}{2} \\ \mu=\frac{10}{2} \\ \mu=5 \end{gathered}[/tex]
E)Find the standard deviation
[tex]\begin{gathered} \sigma=\sqrt{\frac{(b-a)^2}{12}} \\ \sigma=\sqrt{\frac{(9-1)^2}{12}} \\ \sigma=\sqrt{\frac{64}{12}} \\ \sigma=2.309 \end{gathered}[/tex]
F)p(3.5
[tex]P(3.5G)p(x<4.32)[tex]P(x<4.32)=0.415[/tex]
H) *p(x>2.4 | x<7.8)=
[tex]p(x>2.4|x<7.8)=0.675[/tex]
I)p(x>5.97)=
[tex]P(x>5.97)=0.378[/tex]
J)p(x>3.32)=
[tex]P(x>3.32)=0.71[/tex]
K)p(x>7 | x >5)
[tex]P(x>7|x>5)=0.5[/tex]
