Is this a poorly written question?

[adamstr]

Is this a poorly written question?

----
Let X a be a random variable. P[x=0]=.55
For every i >= 0 , P[x=i+1] = 1/3 P[ x=i ]
Find P[ x<=2 ]
----

The answer given (without explanation) is .825, but it is not the answer that I have problems with, it is the question itself. Here is what I am thinking.

X is obviously a Geometric Random Variable. Because it gives the probability for x=0, the distribution must have the form

P[X=x]= q^x * p

That means that P[x=0] = p which implies that p = .55
But they then say that the probability of q is 1/3. (Right? If every probability of x+1 is 1/3 x?)

Any thoughts?

Thanks

[ExamsMakeMeSad]

Is this a poorly written question?

----
Let X a be a random variable. P[x=0]=.55
For every i >= 0 , P[x=i+1] = 1/3 P[ x=i ]
Find P[ x<=2 ]
----

The answer given (without explanation) is .825, but it is not the answer that I have problems with, it is the question itself. Here is what I am thinking.

X is obviously a Geometric Random Variable. Because it gives the probability for x=0, the distribution must have the form

P[X=x]= q^x * p

That means that P[x=0] = p which implies that p = .55
But they then say that the probability of q is 1/3. (Right? If every probability of x+1 is 1/3 x?)

Any thoughts?

Thanks

That's not necessarily true. And even if it were a geometric distribution, P(X<=2) isn't even going to be .825, it'd be 0.909.

Regardless, when you use the intuitive method of calculating this (i.e. .55 + .55/3 + .55/9) you get something like a .794 which isn't even the answer. I am just as stumped as you.

[NoMoreExams]

This doesn't seem like a distribution even because if it was we can sum over all i to get 1 but instead we get

P(X = 0) + P(X = 1) + P(X = 2) + ... = .55 + .55/3 + .55/3^2 + ... = .55[1 + 1/3 + 1/3^2 + ...] = .5/(1 - 1/3) = .825

Are you sure more isn't given?

[adamstr]

[QUOTE=NoMoreExams;80064]This doesn't seem like a distribution even because if it was we can sum over all i to get 1 but instead we get

exactly. no. No more was given.

It is from the actex 15 practice test pack. I am not satisfied with this product, but more on that soon in a different post. (they are too easy, too similiar to each other, ext.)


Note: This problem would make sense if it gave the following probabilities for i>=1