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%.
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