Let's suppose we are considering the experiment of rolling two dice and X is the random variable that tracks the number of one die and Y the number of the other die.
--> What are the distributions of X (and Y) ?
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1Can you clarify what you are confused about? For example, do you know the probability of getting a 1 on the first die? – Pavan C. Apr 22 '21 at 23:15
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To understand why your question was downvoted, you can refer to this article. In fact, you can also refer to this article. – user2661923 Apr 22 '21 at 23:52
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Since (I presume) the dice are uncorollated, i.e., are independent of one another, we obtain that $X$ and $Y$ are independent random variables that attain the values $1$ until $6$ with probability $1/6$ (assuming that the dice are fair and have $6$ faces).
Edit based on comment:
In other words, we have $$\mathbb P(X=k)=\mathbb P(Y=k)=\frac16,\quad k\in\{1,2,3,4,5,6\}.$$ Observe, for example, that $$\sum_{k=1}^6\mathbb P(X=k)=\mathbb P\left(\bigcup_{k=1}^6\{X=k\}\right)=\mathbb P(X\in\{1,2,3,4,5,6\})=1.$$
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Thanks a lot! But how do I write down the distributions? X = {1, 2, ..., 6} or how would you do this? – Lea67 Apr 23 '21 at 06:43
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I've got one last question: the probability that X > 3 knowing that Y = 2 is 1/2, right? – Lea67 Apr 23 '21 at 07:40