Answer:
P ( 1.2 < X < 2.1 ) = 0.3
Step-by-step explanation:
Given:
Uniform distribution over interval (0,3) can be modeled by a probability density function f(x)
f(x) = 1 / (b - a)
Where a < x < b is the domain at which function is defined:
f(x) = 1 / (3) = 1 / 3
Where, X - U ( u , δ )
u = ( a + b ) / 2 = (0 +3) / 2 = 1.5
δ = ( b - a ) / sqrt (12) = (3 - 0) / sqrt (12) = 0.866
Hence,
X - U ( 1.5 , 0.866 )
There-fore calculating P ( 1.2 < X < 2.1 ):
Where, a = 1.2 and b = 2.1
P ( 1.2 < X < 2.1 ) = x / 3 |
P ( 1.2 < X < 2.1 ) = 2.1 /3 - 1.2 / 3 = 0.3
Answer: P ( 1.2 < X < 2.1 ) = 0.3