Thread: Distribute, Expect!

Got a simple question i am trying to solve guys, could definitely do with some help. I am very glad my question will come easy to you guys.

Two numbers are chosen at random from {1,2,3} with repetitions allowed. Let the random variable X denote the sum of the 1st number and 2 times the 2nd number.

(i) Find the Distribution of X.
(ii) Find the Expectation E(X) of X.

Thank you, bad math student trying to catch up

I cant see a clever method to do this, so i'd do it the old fashioned way.

there are only 18 possible outcomes, each with probability 1/18.

Code:

Chosen    |   X   | Prob
1,1,1     |   2   | 1/18
1,1,2     |   4   | 1/18
1,1,3     |   6   | 1/18
2,1,1     |   2   | 1/18
..... etc

As an example, from the incomplete table above, we have:

P(X=2) = 2/18
(it appears twice, each with probability 1/18)

When you do the full table it will appear more times.

Use the same method to work out the chance of X taking all possible values.

Originally Posted by SpringFan25

...we have:

P(X=2) = 2/18
(it appears twice, each with probability 1/18)

"Let the random variable X denote the sum of the 1st number and 2 times the 2nd number." I would guess that the first value of X would be '3' since the first number is one, added with 2 times 1 with a result of two giving 3 as an answer.

I sound like a smartass, but i am getting nowhere >_<

Originally Posted by Aeonitis

Got a simple question i am trying to solve guys, could definitely do with some help. I am very glad my question will come easy to you guys.

Two numbers are chosen at random from {1,2,3} with repetitions allowed. Let the random variable X denote the sum of the 1st number and 2 times the 2nd number.

(i) Find the Distribution of X.
(ii) Find the Expectation E(X) of X.

Thank you, bad math student trying to catch up

(1,1)...1+2(1)=3
(2,1)...2+2(1)=4
(3,1)...3+2(1)=5
(1,2)...1+2(2)=5
(2,2)...2+2(2)=6
(3,2)...3+2(2)=7
(1,3)...1+2(3)=7
(2,3)...2+2(3)=8
(3,3)...3+2(3)=9

Finally E(X) is the mean or average of X (the sums)

Awesome Archie, and that is the full answer, THAT SIMPLY?! oh, just making sure, i mean the right answer would be that the expectation of X i.e. E(X) is 54/9 giving a result of 6?!

Originally Posted by Aeonitis

Awesome Archie, and that is the full answer, THAT SIMPLY?! oh, just making sure, i mean the right answer would be that the expectation of X i.e. E(X) is 54/9 giving a result of 6?!

Yes, that's it..
As the saying goes..."it's easy when you know how"...

Or when you understand the lexicon.