probability density function for discrete variables

[soulie]

May I know how to get the expectation or the expected value for this one? Having a variable for the f(x) in discrete variables was not taught to us.
Any thorough explanation will be enough. Thank you

 

[BigBeachBanana]

View attachment 31896
May I know how to get the expectation or the expected value for this one? Having a variable for the f(x) in discrete variables was not taught to us.
Any thorough explanation will be enough. Thank you

I'm confused by the question. The variable is Y, what does x=1,2,3... have to do what the density function?

 

[Otis]

I note that Y and y are two different variable symbols. I wonder whether that's a mistake.

[imath]\;[/imath]

 

[LCKurtz]

Supposing there is simply a typo, perhaps the problem is meant to be:
[math]P(Y=y) = p^y,~y= 1,2,3,...[/math] where [imath]p = \frac 1 2[/imath]. Then the problem is apparently just calculating [imath]\sum_{y=1}^\infty yp^y[/imath].
Hint: What do you get if you differentiate[math]\sum_{y=1}^\infty p^y = \frac p {1-p}[/math] with respect to [imath]p[/imath]? See if that helps. You can put [imath]p=\frac 1 2[/imath] in later.