CFA Practice Question

There are 410 practice questions for this study session.

CFA Practice Question

You are given a discrete random variable, X, which has the following distribution: p(X=0, 1%, 2%, or 3%) = 25%, P(X > 3%) = 50%; P(X < 0) = 50%. Does this function satisfy the conditions for a probability function?

A. No
B. Yes
C. Not enough information to tell
Correct Answer: A

The two key requirements for a probability function are that 0 <= p(x) <= 1 and that the sum of the probabilities p(x) over all possible values of X is equal to 1. This function meets the first test but fails the second test. The second test fails because the sum of the probabilities equals 4 * 0.25 + 0.5 + 0.5 = 2.0

User Contributed Comments 10

User Comment
guai 0.25+0.5+0.5=1.25 > 1
pranit Even first condition is not satisfied because probability of any event cannot be negative and in the question it says P(X<0)=50%.
mordja You are misreading it pranit.

You can have a result that is less than zero, but you cant have a probability that is less than zero, or greater than one.

What you refer to was that the result 'x' would be less than zero, not the probability.
thekid DON'T Agree with "4*0.25"....

Doesn't this "P(x=0,1,2 or 3)=0.25" mean that the Probability that X equals either 0,1,2 or 3 is .25 which translates to P(x=0)= .0625 and P(x=1)=.0625 and P(x=2)=.0625 and P(x=3)=.0625 {.25 dived by 4}. So, how come when they summed up the probability they got 4 TIMES .25?

It should just be .25 + 0.5 + 0.5 = 1.25 OR 4*0.0625 + 0.5 + 0.5 = 1.25

PLEASE HELP!!!
Thanks.
hardig thekid-I think the first probablility is a 25% chance of being 0, 1, 2 or 3 = which translates into the 4*0.25 - then there is 0.5 change of being greater than 3 and a 0.5 chance of being less than 0. Therefore (0.25+0.25+0.25+0.25)+0.5+0.5=2.
johntan1979 Agree with thekid.

P(A or B) = P(A) + P(B) - P(AB) and in this case, P(AB) = 0, since X cannot be 1% and 2% (for example) at the same time.

Therefore, P(X=0, 1%, 2%, or 3%) = 0.25, not 4x0.25
dmfz if P(X>3%) = 50%
but P(X = 0,1%,2%,3%) then the obvious answer is NO, since the parameters of X are ONLY 0,1,2,3.
JMORALES thekid: The question reads "p(X=0, 1%, 2%, or 3%) = 25%" The word 'OR' is the indicator that .25 belongs to each value of X, hope this helps
JMORALES thekid: p(X=0, 1%, 2%, or 3%) = 25%, the word OR is the indicator that .25 belongs to each value of x
khalifa92 mutually exclusive and exhaustive summed to 1
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