MHB A Strange Probability Exercise

[Greekguy]

Hello and I would like to thank you for your space in this website

I'm from Greece and i have exams in next days

I need some help with an exercise that I can not solve!

There is a probability density function with the following type :

P(Y=y/X=x)=f(y,x)= $${n \choose y}* {x}^{y} * ({1-x})^{n-y}=\begin{cases} \\ \end{cases}$$ (i don't know how to delete the last two symbols the "=" and the "{")
y=0,1,2,,,n

f_xX=1 for 0<=x<=1 and f_xX=0 in other space. Find E(Y)I wish that there is someone who could help me with this mountain!

Thank you !

 

[Euge]

Hi, Greekguy! (Wave)

It's not clear what $f_x$ represents, because it does not relate to the conditional probability density $f(y,x)$. Could you be more explicit?

 

[Greekguy]

Hi, Greekguy! (Wave)

It's not clear what $f_x$ represents, because it does not relate to the conditional probability density $f(y,x)$. Could you be more explicit?

Thank you so much with your time! i exprees the exercise with a photo and if you can, help me :)View attachment 6370