Joint distribution of a discrete random variable

In summary, The conversation is about a problem involving an urn with 6 numbered balls and the minimal and maximal numbers seen when taking out 4 balls. The question is about calculating the probabilities for different combinations of X and Y values.
  • #1
Yankel
395
0
Hello all

I have this question I am trying to solve.

In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement.

X - the minimal number we see
Y - the maximal number we see

I need to joint distribution.

I understand that X is getting the values 1,2,3 while Y 4,5,6.

The problem is calculating the probabilities. How do I calculate the probability that X = 1 and Y = 5 ? What about the probability that X = 2 and Y = 6 ? And so on...

thanks !
 
Mathematics news on Phys.org
  • #2
Yankel said:
Hello all

I have this question I am trying to solve.

In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement.

X - the minimal number we see
Y - the maximal number we see

I need to joint distribution.

I understand that X is getting the values 1,2,3 while Y 4,5,6.

The problem is calculating the probabilities. How do I calculate the probability that X = 1 and Y = 5 ? What about the probability that X = 2 and Y = 6 ? And so on...

thanks !

Hi Yankel,

How about enumerating them all?
There are only $\binom 6 4 = 15$ possible combinations.
 
  • #3
A little bit hard to count them all, but it works ! Thanks
 

FAQ: Joint distribution of a discrete random variable

1. What is a joint distribution of a discrete random variable?

A joint distribution of a discrete random variable refers to the probability distribution of two or more discrete random variables occurring simultaneously. In other words, it shows the probabilities of various outcomes for multiple variables occurring together.

2. How is a joint distribution different from a marginal distribution?

A joint distribution takes into account the probabilities of multiple variables occurring together, while a marginal distribution only considers the probabilities of a single variable occurring.

3. How is a joint distribution calculated?

A joint distribution is calculated by multiplying the probabilities of each possible outcome for each variable. For example, if variable X can have values of 1, 2, or 3 with probabilities 0.2, 0.3, and 0.5 respectively, and variable Y can have values of 4, 5, or 6 with probabilities 0.1, 0.4, and 0.5 respectively, the joint distribution would be 0.2*0.1=0.02 for X=1 and Y=4, 0.3*0.4=0.12 for X=2 and Y=5, and so on.

4. What information can be inferred from a joint distribution?

A joint distribution can provide information about the relationship between multiple variables, such as whether they are positively or negatively correlated. It can also be used to calculate the probabilities of specific combinations of values occurring.

5. Can a joint distribution be used to make predictions?

Yes, a joint distribution can be used to make predictions about the likelihood of specific combinations of values occurring for multiple variables. This can be useful in various fields such as finance, economics, and engineering.

Similar threads

Getting the probability distribution of a random variable
Replies
2
Views
690
I Linear regression and random variables
Replies
30
Views
3K
MHB Win a $10 or $5 Prize in Tom's 4/19 Lottery Fundraiser
Replies
1
Views
2K
I Random variable and elementary events
Replies
9
Views
2K
I Random variable and probability
Replies
5
Views
1K
B Definition of a random variable in quantum mechanics?
Replies
12
Views
1K
MHB Calculation of probability with arithmetic mean of the sum of random variables
Replies
1
Views
2K
I Sampling theory and random sample
Replies
5
Views
2K
MHB Random Variables: Proving Same Probability Distribution & Finding $X+Y$
Replies
11
Views
3K
Prob/Stats Probability book for basic understanding
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top