A continuous random variable X is uniformly distributed. The minimum value for X is 20 and the maximum value for X is 120.
Write down the rules for f(x), the density function for X.
Find the median of this distribution.
Find P(X>40)
Find P( 25 < X < 55)
Find P(X < 75)
a) We are given here that the distribution is uniform from 20 to 120, therefore the distribution here is given as:
Therefore the probability density function for X here is obtained as:
This is the required PDF here.
b) The median of the distribution here is computed as:
Therefore 70 is the required median here.
c) The probability here is computed as:
Therefore 0.8 is the required probability here.
d) The probability here is computed as:
Therefore 0.3 is the required probability here.
e) The probability here is computed as:
Therefore 0.55 is the required probability here.
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