CFA CFA Level 1 Quants: Study Session 3, LOS 9.i

# Quants: Study Session 3, LOS 9.i

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• peekabooitsme
Participant
• CFA Level 3
1

I am in the process of debriefing a practice exam and confused on the answer.
Question: A continuous uniform distribution is bounded by zero and 20. The probability of an outcome equal to 12 is closest to:
a. 0.00
b. 0.05
c. 0.60

I put 0.05 because 1/20 chance of getting any random variable in the range.

However the answer key say 0.00 because the distribution is continuous, the probability of any specific outcome is zero.

If the question didn’t have the word “uniform” I would get it – but now I am just confused.

• 2

If the question asked for F(12) then you can answer it by thinking of it as P(x<=12), or, 12*(1/20).

• 1

Hi @peekabooitsme, I believe the word “uniform” simply means that not only the distribution is continuous (i.e. not discrete or “lumpy”), but also the probability of the outcome being in any two intervals of the same size will be equal (as long as the intervals are within the range — between zero and 20 in this example. This is different from the Normal distribution, which is also continuous but not uniform: it is more likely that the outcome is closer to the center of the distribution (i.e. near the mean) than towards the tails.

In any case, it is the fact that the distribution is continuous that makes the answer (a) or 0.00 — the question mentions the probability of a single outcome — it’s like the length of a “point” — as opposed to the probability of an interval which would definitely be different than zero if the interval is within the range of the distribution.

Hope this helps!

• 1

yep, @edulima is right…all you need to see for such questions is whether it is discrete or continuous, @peekabooitsme

• 0

Key word continuous. Don’t over-think it. When distribution is continuous probability of any particular number is 0. The rest is just unnecessary noise.