Let X be a continuous random variable uniformly distributed on the interval (0,b). The density function of X is given by:
1/b for 0<x<b,
0 otherwise
If 0<a<x<b, evaluate the conditional probability P(X less than or equal to x|X>a).
Let X be a continuous random variable uniformly distributed on the interval (0,b). The density function of X is given by:
1/b for 0<x<b,
0 otherwise
If 0<a<x<b, evaluate the conditional probability P(X less than or equal to x|X>a).
The graph. the ordinates at x=0 and x=b and the x-axis make a rectangle, length b, height 1/b
Areas represent probability. You are given X>a so you know which part of the rectangle you are in. So x is between x=a and x=b
So you want to know fraction the rectangle with base x-a is of the rectangle with base b-a