Question

Suppose the reaction temperature X (in deg C) in a certainchemical process has uniform distribution with A= -5 and B=5.

a. Compute P(X<0)
b. Compute P(-2.5 c. Compute P(-2

Answer 1

Explanation:

Given that the reaction temperature X (in deg C) in a certainchemical process has uniform distribution with A= -5 and B=5

Thus the pdf of X would be

`f(x) = 0.1 , -5\leq x\leq 5`

the cumulative probability

`F(x) = (x-a)/(10) ,-5\leq x\leq 5`

a) P(X<0) = F(0) =
`(0-(-5))/(10) =0.5`

b) P(x<-2.5) = F(-2.5)

=
`(0-(-2,5))/(10) =0.25`

c) P(X>-2) = 1-F(-2)

=1-0.2 = 0.8