Question

B)Graph the probability distribution C)Find the probability density function p(x)=D)Find the mean E)Find the standard deviation F)p(3.52.4 | x<7.8)=I)p(x>5.97)=J)p(x>3.32)=K)p(x>7 | x >5)

Answer 1

Given

Uniform distribution

a = 1

b = 9

Procedure

B) Graph the probability distribution

C)Find the probability density function p(x)=

`\begin{gathered} p(x)=(1)/(b-a) \\ p(x)=(1)/(8) \\ p(x)=0.125 \end{gathered}`

D)Find the mean

`\begin{gathered} \mu=(a+b)/(2) \\ \mu=(9+1)/(2) \\ \mu=(10)/(2) \\ \mu=5 \end{gathered}`

E)Find the standard deviation

`\begin{gathered} \sigma=\sqrt{((b-a)^2)/(12)} \\ \sigma=\sqrt{((9-1)^2)/(12)} \\ \sigma=\sqrt{(64)/(12)} \\ \sigma=2.309 \end{gathered}`

F)p(3.5

`P(3.5G)p(x<4.32)[tex]P(x<4.32)=0.415`

H) *p(x>2.4 | x<7.8)=

`p(x>2.4|x<7.8)=0.675`

I)p(x>5.97)=



`P(x>5.97)=0.378`

J)p(x>3.32)=



`P(x>3.32)=0.71`

K)p(x>7 | x >5)

`P(x>7|x>5)=0.5`