The Student Room Group

S1 Discrete Random Variables

The random variable X has the following distribution:

x 1 2 3
P(X=x) a b a

where a and b are constants.
a) write down E(X)
b)given that Var(X)= 0.75, find the values of a and b
Original post by DeathstrokeXL79
The random variable X has the following distribution:

x 1 2 3
P(X=x) a b a

where a and b are constants.
a) write down E(X)
b)given that Var(X)= 0.75, find the values of a and b


What have you tried?
Original post by RDKGames
What have you tried?


I found out E(X) by multiplying x with their probabilities and found out (E(x))^2 and E(X^2) but I got the answers in the form of a and b while in the answers, it is given as "2 by symmetry" what does this mean and how do I do this. I would appreciate it if any of you show me the working to it as well
Original post by DeathstrokeXL79
I found out E(X) by multiplying x with their probabilities and found out (E(x))^2 and E(X^2) but I got the answers in the form of a and b while in the answers, it is given as "2 by symmetry" what does this mean and how do I do this. I would appreciate it if any of you show me the working to it as well


This distribution is symmetric. Notice that the probability aa appears twice, and bb is wedged in between. So expectation is precisely the middle one.
Original post by RDKGames
This distribution is symmetric. Notice that the probability aa appears twice, and bb is wedged in between. So expectation is precisely the middle one.


I don't understand it completely. Can you please explain what you just said?

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