Consider a random variable,X,with Uniform density over the range 0 to 3.What is P(1.2

Question

Consider a random variable,X,with Uniform density over the range 0 to 3.What is P(1.2 < X < 1.8)?
A)1.00
B)0.20
C)0.60
D)0.40
E)0.50

Quizplus · Accepted Answer

For a uniform distribution over the range 0 to 3, the total range is 3 - 0 = 3. The probability density function is constant over this range, so the probability of an event occurring within a subinterval of the range is simply the length of that subinterval divided by the total length of the range. Here, the subinterval is from 1.2 to 1.8, which has a length of 1.8 - 1.2 = 0.6. Therefore, the probability is 0.6 / 3 = 0.20.

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