# Thread: Find the distribution

1. ## Find the distribution

Hi, hopefully someone can help me with this question, not sure what it is I'm supposed to do exactly.

Let $X_1$ and $X_2$ be independent random variables with common distribution defined by:

$X =$
0, with probability $\frac{1}{8}$
1, with probability $\frac{3}{8}$
2, with probability $\frac{1}{2}$

Find the distribution of the sum of $X_1 + X_2$

Hopefully someone can point me in the right direction with this

Craig

2. Originally Posted by craig
Hi, hopefully someone can help me with this question, not sure what it is I'm supposed to do exactly.

Let $X_1$ and $X_2$ be independent random variables with common distribution defined by:

$X =$
0, with probability $\frac{1}{8}$
1, with probability $\frac{3}{8}$
2, with probability $\frac{1}{2}$

Find the distribution of the sum of $X_1 + X_2$

Hopefully someone can point me in the right direction with this

Craig
Let $Y = X_1 + X_2$. What are the possible values of $Y$? What values of $X_1$ and $X_2$ give those values? Therefore, what is the probability of those values of $Y$?

3. Originally Posted by mr fantastic
Let $Y = X_1 + X_2$. What are the possible values of $Y$? What values of $X_1$ and $X_2$ give those values? Therefore, what is the probability of those values of $Y$?
$Y = X_1 + X_2$, therefore $Y$ can take the values 0..4.

$P(Y=0) = \frac{1}{8}\times\frac{1}{8} = \frac{1}{64}$

$P(Y=1) = 2(\frac{3}{8}\times\frac{1}{8}) = \frac{3}{32}$

$P(Y=2) = \frac{17}{64}$

$P(Y=3) = \frac{3}{8}$

$P(Y=4) = \frac{1}{4}$

Is this what you meant to do?

Thanks for the reply

4. Originally Posted by craig
$Y = X_1 + X_2$, therefore $Y$ can take the values 0..4.

$P(Y=0) = \frac{1}{8}\times\frac{1}{8} = \frac{1}{64}$

$P(Y=1) = 2(\frac{3}{8}\times\frac{1}{8}) = \frac{3}{32}$

$P(Y=2) = \frac{17}{64}$

$P(Y=3) = \frac{3}{8}$

$P(Y=4) = \frac{1}{4}$

Is this what you meant to do?

Thanks for the reply
Yes.

5. Originally Posted by mr fantastic
Yes.
Thanks again