Question : Two discrete random variables X and Y have joint pmf given by the following table:
i) Find C
ii) Compute the probability of each of the following events.
- X 1 1/2
- X is odd
- XY is even
- Y is odd given that X is odd
Question : Two discrete random variables X and Y have joint pmf given by the following table:
i) Find C
ii) Compute the probability of each of the following events.
- X 1 1/2
- X is odd
- XY is even
- Y is odd given that X is odd
What are you having problems with specifically with this problem? What have you tried so far? For the first part its a simple application of the fact that given the sample space S, P(S)=1.
As for the second part, I would first compute the marginal probabilities of X and Y, and see if that helps you knock out some of those problems.
Remember that the probability that an outcome occurs in a sample space is 1 (or 100% chance that some event is going to happen). So if you know that the Probability of X and Y occurring MUST add up to 1, and you have all probabilities except for C, how do you go about figuring out what C is?
Here is what u have done till now....
C = ..........Is that correct?
Could u please explain me what does 'X is odd' mean, i tried searching on the net for the term odd random variable but couldnt find any meaning ...........please explain me when is a random variable termed odd or even
I think you are confusing yourself with what the question is asking. Not to be blunt, but literally, you are being asked for the random variables whose values are odd (i.e. not even, not divisible by 2). If I asked you to toss a dice, and give me the probability of getting an ODD NUMBER, how would you go about that? This question is no different:
The probability of X being odd is P(X=1 or X=3).
The probability of the random variable XY being odd is P(XY=1, 3, 9).
The last one is a conditional. Do you know how to compute marginal probabilities? What is the probability of X being equal to 1 over ALL values of Y (since this is a joint pdf)? That is the probability of X being equal to 1. We call them "marginals", because you would (to make it less messy) scribble the total probabilities in the "margins" of your chart there. Once you compute the marginal, it is simple to compute P(Y|X is odd).