Question

Consider a uniform distribution from aequals=44 to bequals=2828. ​(a) Find the probability that x lies between 1111 and 2424. ​(b) Find the probability that x lies between 99 and 2222. ​(c) Find the probability that x lies between 77 and 1919. ​(d) Find the probability that x lies between 1010 and 2323.

Answer 1

Answer with explanation:

Given : The interval for a uniform distribution : (4, 28)

The density function for the uniform distribution will be :-

`f(x)=(1)/(28-4)=(1)/(24)`

(a) Required interval : (11,24) =
`24-11=13`

Now, the probability that x lies between 11 and 24 is given by :-

`=\text{(Required interval)} \cdot\ f(x)=(13)/(24)`

(b) Required interval : (9,22) =
`22-9=13`

Now, the probability that x lies between 9 and 22 is given by :-

`=(13)/(24)`

(c) Required interval : (7,19) =
`19-7=12`

Now, the probability that x lies between 9 and 22 is given by :-

`=(12)/(24)=0.5`

(d)Required interval : (10,23) =
`23-10`

Now, the probability that x lies between 9 and 22 is given by :-

`=(13)/(24)`