Consider a random variable,X,with Uniform density over the range 0 to 1. What is P(0.2

Question

Consider a random variable,X,with Uniform density over the range 0 to 1.  What is P(0.2 < X < 0.5 and 0.4 < X < 0.6)?
A)1.00 
B)0.40 
C)0.10 
D)0.50 
E)0.00

Quizplus · Accepted Answer

Since the density of X is uniform over the range 0 to 1, the probability of X being between 0.2 and 0.5 is (0.5-0.2)/1 = 0.3 and the probability of X being between 0.4 and 0.6 is (0.6-0.4)/1 = 0.2. The intersection of these two events is between 0.4 and 0.5, which has a probability of (0.5-0.4)/1 = 0.1. Therefore, P(0.2 < X < 0.5 and 0.4 < X < 0.6) = P(0.4 < X < 0.5) = 0.1. The answer is C.

Consider a Random Variable,X,with Uniform Density Over the Range 0