The hardness of a certain alloy measured on the Rockwell sca

The hardness of a certain alloy (measured on the Rockwell scale) is a random variable X. Assume that X UNIF (50, 75). (a) Give the CDF of X. (b) Fine P[60

Solution

X~ Unif( 50 , 75 )....

a) cdf : 0 if x < 50... ;
(x-50) / 25 if 50 < x < 75......
   1 if x>=75....

b) p( 60 < X < 70 ) = integration from 60 to 70 [ dx / 25 ] = 0.4............

c) E(X) = 0.5 ( 50 + 75 ) = 62.5.........

d) var(X) = ( 75 - 50)^2 / 12 = 52.0833333.........