A random variable follows the continuous uniform distribution between
30
and
120
a) Calculate the probability below for the distribution.
P(60less than or equals≤xless than or equals≤90)
b) What are the mean and standard deviation of this distribution?
wo neng kan jian wen ti
Part a)
P ( 60 < X < 90 ) = ( 60 - 90 )/ ( 120 - 30 )
P ( 60 < X < 90 ) = 0.3333
Part b)
Mean ( X ) = ( a + b )/ 2
Mean ( X ) = ( 30 + 120 )/ 2
Mean ( X ) = 75
Variance ( X ) = ( b - a )2 / 12
Variance ( X ) = ( 120 - 30 )^2 / 12
variance ( X ) = 675
Standard Deviation =
Standard Deviation = 25.9808
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