1. ## Random variables

If a random variable X is defined as X =

{2 if heads on first toss
{-1 if tails on first toss

and I want to find the mean of 2X, how do I go about doing this?

Is it 2(2)(1/2) + 2(-1)(1/2)?

Also, I know this mean won't be negative, but is it possible to have a negative mean from a random variable?

2. Originally Posted by noles2188
If a random variable X is defined as X =

{2 if heads on first toss
{-1 if tails on first toss

and I want to find the mean of 2X, how do I go about doing this?

Is it 2(2)(1/2) + 2(-1)(1/2)?

Also, I know this mean won't be negative, but is it possible to have a negative mean from a random variable?
Assuming that the experiment is tossing a fair coin however many times, with the RV X being defined for only the first toss, then you did this right. And yes, it is very possible for a RV to have a negative mean.

Try to define the experiments clearly. It's obvious what is going on in this case, but it can be very hard to answer probability questions helpfully when the design of the experiment is ambiguous.

3. Yes, this was a fair coin tossed once. In the future, I will be more clear. Thank you for your help.