Question

Set A consists of the ten digits 0,0,0,0,0,0,2,2,2,4.
Set B consists of the seven digits 0,0,0,0,2,2,2.
One digit is chosen at random from each set. The random variable X is defined as the sum of these two digits.
(i) Show that P(X=2)=3/7
(ii)Tabulate the probability distribution X
(iii)Find E(X) and Var(X)
(iv)Given that X=2, find the probability that the digit chosen from set A was 2

Answer 1

please help... I'm confused here 0_0

Answer 2

Need help?

Answer 3

First, let's start with "i". And, for simplicity, lets say that choosing from set A is signified by the random variable "A" (and "B" for set B).
That means that
X = A+B

Well, "i" is simple because there are only two ways that X can equal "2":
Either A=0 and B=2
Or A=2 and B=0

So calculate the probability of these two events and add them together:

\[\frac{ 3 }{ 5 }*\frac{ 3 }{ 7 }+\frac{ 3 }{ 10 }*\frac{ 4 }{ 7 } = \frac{ 3 }{ 7 }\]

With me so far?

Answer 4

yes :D now i understand where you get the values