Question

The annual amount of rainfall in Ventura County is bounded by 6.3 and 20.5, is continuous and each outcome is equally likely. Use this information to answer the following four questions.

a. Determine P(10.2 < x < 18.7).
b. Determine P(x > 17.1).
c. Determine P(x < 6.3).
d. What is E[x]?

Answer 1

a.0.5984

b.0.2394

c.0

d.13.4

Explanation:

We are given that

a=6.3,b=20.5

The pdf of uniform distribution

`f(x)=(1)/(b-a)=(1)/(20.5-6.3)=0.0704`,6.3<x<20.5

0, otherwise

Now,

a.

P(10.2<x<18.7)=
`\int_(10.2)^(18.7)f(x) dx`

`=0.0704[x]^(18.7)_(10.2)`

`P(10.2<x<18.7)=0.0704(18.7-10.2)=0.5984`

b.P(x>17.1)

`P(x>17.1)=\int_(17.1)^(20.5)0.0704dx`

`=0.0704(20.5-17.1)`

`=0.2394`

c.P(x<6.3)=0

d.E[x]=
`(a+b)/(2)=(6.3+20.5)/(2)=13.4`