- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions
- Subject 2. Probability Function
CFA Practice Question
The random variable X has the following distribution:
f(x) = [c(6 - x)]/10, x = 0,1,2,3
B. 5/9
C. 18/10
f(x) = [c(6 - x)]/10, x = 0,1,2,3
What value of c makes this a legitimate probability distribution?
A. 3/10
B. 5/9
C. 18/10
Correct Answer: B
For this to be a legitimate probability distribution, Σ p(x) = 1, so c = 5/9.
User Contributed Comments 12
| User | Comment |
|---|---|
| Gina | [c(6-0)/10]+[c(6-1)/10]+[c(6-2)/10]+[c(6-3)/10]=1 18c=10 c=5/9 |
| noonah | Is there a way to do this on BAII? |
| Janey | I think you could also answer that there are 4 probablities 0,1,2,3. All probability distributions = 1, so (4+5)/9 = 1. i could be wrong tho?? |
| Bibhu | Janey u are right. Better way to answer is as provided by Gina. |
| whiteknight | so the best way to solve these kind of questions is to substitute and see ? |
| steved333 | Gina and Janey are both right. Janey's pretty good with the shortcuts, and Gina, thank you for your detailed clarification. Understanding it makes it easier to remember it... |
| JanLani | Gina's step through helped simplify and clarify it a lot. Thanks |
| tschorsch | Janey's answer does not make sense. The for probabilities are the four values of f(x) after substitution of x and c. You must solve for c. There is no short cut. |
| alallstar | yeah i don't quite get janey's solution either. |
| johntan1979 | No shortcuts, and definitely a time-waster. |
| gill15 | not a time waster and takes maybe 30 seconds.....its a discrete probability that only has values for x = 0, 1, 2 and 3. just sub in each value of x into the p(x) given...sum each one and equate to 1....just like gina did... |
| minhnhut | Disregard C and sub value in, we have (6+5+4+3)/10=9/5 The only value to make the sum 1 is 5/9 |