Question

Which of the following statements is not true about continuous probability distributions?

Select one:

a. The probability of any event is the area under the density curve over the range of values that make up the event.

b. The total area under the density curve must be exactly 1.

c. If X is a continuous random variable taking values between 0 and 500, then
P(X > 200) = P(X ? 200).

d. There are no disjoint events in continuous probability models.

Answer 1

a) Whatever outcomes are included in the event, we look at the area under these outcomes to find the required probability. This statement is TRUE

b) Total probability is always 1, therefore total area under the density curve should always be 1.  This statemetn is TRUE

c) For a continuous random variable P(X = 200) = 0 at discrete point. This statement is TRUE

d) There could be disjoint events in the continuous probability models, for example in a uniform distribution U(0, 10), then 0 < X < 2 and 5 < X < 6 would be disjoint events.

Therefore d) is the correct answer here.