If the random variable x is uniformly distributed between 40 and 60, then, calculate p(35 < x < 45)?

Solution:

The random variable x is uniformly distributed between 40 and 60 [Given]

f(x) = 0 if x < 40

1/(60 - 40) = 1/20 if 40 <= x <= 60

0 if x > 60

P (35 < x < 45) = \(\int {(1/20)dx}\) for 35 < x < 45

= [ (1/20)X ], 35 < x < 45

= (1/20)[45 - 35]

= 10/20

= 1/2

= 0.5

= 50%

Therefore, p(35 < x < 45) is 50%.

If the random variable x is uniformly distributed between 40 and 60, then, calculate p(35 < x < 45)?

Summary:

If the random variable x is uniformly distributed between 40 and 60, then p(35 < x < 45) is 50%.