# Thread: Error in probability question?

1. ## Error in probability question?

Hi guys,

I believe there are one or two errors in the wording of this problem and I need to make sure I know what they are before I actually do this problem. The problem reads:

Suppose that $\displaystyle R$ is a random variable $\displaystyle f_R(x) =\frac{3}{8}x^2$ for $\displaystyle x \in [0, 2]$ Let $\displaystyle Y = X^3$
(a) Find $\displaystyle F_Y(y)$

(b) Find $\displaystyle f_y(y)$

Would it make more sense for the problem to read "Suppose that $\displaystyle X$ (instead of $\displaystyle R$)is a random variable..." and $\displaystyle f_X(x) = \frac{3}{8}x^2$ instead of $\displaystyle f_R(x) = \frac{3}{8}x^2$?

Also, for (a) and (b), did the author mean "Find $\displaystyle F_Y(x)$" and "Find $\displaystyle f_Y(x)$" instead of $\displaystyle F_Y(y)$ and $\displaystyle f_Y(y)$ respectively?

Thanks for any help!

James

2. ## Re: Error in probability question?

Originally Posted by james121515
Hi guys,

I believe there are one or two errors in the wording of this problem and I need to make sure I know what they are before I actually do this problem. The problem reads:

Suppose that $\displaystyle R$ is a random variable $\displaystyle f_R(x) =\frac{3}{8}x^2$ for $\displaystyle x \in [0, 2]$ Let $\displaystyle Y = X^3$
(a) Find $\displaystyle F_Y(y)$

(b) Find $\displaystyle f_y(y)$

Would it make more sense for the problem to read "Suppose that $\displaystyle X$ (instead of $\displaystyle R$)is a random variable..." and $\displaystyle f_X(x) = \frac{3}{8}x^2$ instead of $\displaystyle f_R(x) = \frac{3}{8}x^2$?

Also, for (a) and (b), did the author mean "Find $\displaystyle F_Y(x)$" and "Find $\displaystyle f_Y(x)$" instead of $\displaystyle F_Y(y)$ and $\displaystyle f_Y(y)$ respectively?

Thanks for any help!

James
R is a random variable that depends on x. There's nothing wrong with that, it's just unusual notation.

(a) and (b) are correctly stated in the question.

3. ## Re: Error in probability question?

To clarify, $\displaystyle f_R(x)$ is the probability density function for the random variable $\displaystyle R$ (or $\displaystyle X$, and big $\displaystyle X$ and big $\displaystyle Y$ are random variables as well. Not sure if that changes anything?

4. ## Re: Error in probability question?

Originally Posted by james121515
To clarify, $\displaystyle f_R(x)$ is the probability density function for the random variable $\displaystyle R$ (or $\displaystyle X$, and big $\displaystyle X$ and big $\displaystyle Y$ are random variables as well. Not sure if that changes anything?
I have given my opinion on the wording of the question as posted in post #1. I do not understand your so-called clarification. Are you saying the question is NOT as worded in post #1?

5. ## Re: Error in probability question?

The question is worded exactly as in the original post, except for a small typo on my part it should have been:

(b) $\displaystyle f_Y(y)$ and not $\displaystyle f_y(y)$

If the wording of the problem is correct, could you please help me understand the question. Since our pdf $\displaystyle f_R(x)$ is for the random variable $\displaystyle R$, woudn't we need some relationship between $\displaystyle R$ and $\displaystyle X$, and then from $\displaystyle X$ to $\displaystyle Y$ (which we have since $\displaystyle Y=X^3$) in order to do this?

Best,
James

6. ## Re: Error in probability question?

Originally Posted by james121515

The question is worded exactly as in the original post, except for a small typo on my part it should have been:

(b) $\displaystyle f_Y(y)$ and not $\displaystyle f_y(y)$

If the wording of the problem is correct, could you please help me understand the question. Since our pdf $\displaystyle f_R(x)$ is for the random variable $\displaystyle R$, woudn't we need some relationship between $\displaystyle R$ and $\displaystyle X$, and then from $\displaystyle X$ to $\displaystyle Y$ (which we have since $\displaystyle Y=X^3$) in order to do this?

Best,
James
OK, looking at it closer I see what you mean. It would make sense to be asked to find the pdf for Y = R^3 since the question does not define the random variable X anywhere.

I suggest you ask whoever set the question. I recant my earlier opinion and would suggest there is a typo in the definition of Y.