Question

What is the marginal probability of X = 2?

Answer 1

so, lets start with 7.

X can take values: 1 ,2
Y can take values: 1 ,2

They asked what is f(x,y), when x =2 and y =2

so you just plug in x=2 and y =2 in f(x,y)

4/(9*2*2) = .. .

Answer 2

then we got to 8.

They asked the probability when X takes the value =2.
What about Y?? it can still take the value =1 OR =2
(It can't take both values at the same time!)

so in f(x,y), plug in x=2, y=1
then plug in x=2,y=2
and just add them!

Answer 3

Why 1 and 2 though? where did those values come from.. For the number 7, I just overcomplicated myself.

Answer 4

and which formula do I have to plug them into? the same as before?
4/(9*x*y) = .

Answer 5

Its given in Question 7, that they can take values 1 and 2.

Q 7,8,9 are dependent

Answer 6

yes, that formula applies for all those questions

Answer 7

I didn't know they were dependent... They were confusing! `Usually they just repeat the question.

Answer 8

True, it should be mentioned.
just asking for marginal probability of X=2, is absurd!

Answer 9

Yes that is! I was so confused. But I believe it's true

Answer 10

so what did you get for question 7 and 8 ?

Answer 11

For 7, I got 1/9 and the 8 , 1/3
Is that correct?

Answer 12

absolutely :)
need help with 9th one too?

Answer 13

Yes please! Was just about to ask
You're awsome by the way!

Answer 14

good learners like you make me awesome ^_^

So the definition of Conditional probability
\(\Large P(A|B) = \dfrac{P(A\cap B)}{P(B)}\)

we need, P(Y=1 | X=1)

Answer 15

so using the formula,

we actually need,
\(\Large \dfrac{P(Y=1 \quad and \quad X=1)}{P(X=1)}\)

makes sense?

Answer 16

the |
is read as 'given'

Answer 17

And P stands for Probability. Is it also refering again to the first Function from question 7?

Answer 18

yes, and yes!

the numerator is same as 7th question, with values changed.
the denominator is same as 8th question, with values changed!

Answer 19

So numeratior is 4/9

Answer 20

correct :)
get the denominator now

Answer 21

2/3?

Answer 22

yup,
so whats the answer for 9th?

Answer 23

1 :)

Answer 24

the numerator is 4/9
and denominator is 2/3

try again?

Answer 25

2/3 lol. Sorry

Answer 26

\(\huge \checkmark\)

Answer 27

Thanks a whole lot!!

Answer 28

welcome ^_^
happy to help :)

Answer 29

Can I ask one last question?

Answer 30

What would be the probability of X=1 and Y=1 assuming that X and Y are independent? -- with the same 4/9(xy) - Just don't understand what the independence has to do with anything...

Answer 31

Independent events means one even does not depend on other...

so X being = 1, does not depend on whether Y=1 or 2

if 2 events A,B are independent,
then
\(\Large P(A \cap B) = P(A) \times P(B)\)

Answer 32

they are asking P(X=1 and Y=1)

find P(X=1) and P(Y=1) separately,
and just multiply them!

(You already got P(X=1) in question 9 :) )

Answer 33

2/3 for P(x=1) ... so now finding y?

Answer 34

Am I thinking wrong or is Y=1 the same? 2/3?

Answer 35

it would be same, because if you interchange x and y, you still get same f(x,y)!

so both P(X=1) = P(Y=1) = 2/3
just multiply them :)

Answer 36

so that's just 4/9 :) Easier than I thought. Should stop overcomplicating things!

Answer 37

yup :)
good luck!

Answer 38

Thank you!!!

Answer 39

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