Understanding Joint Density Functions: Solving for Unknown Parameters

[wuid]

it seems that i can't understand the boundaries...
the joint density function:

f(u,v)= a , u^2 <= v <= 1
0 , else

find a

i just don't know how to start.
any help ?
thx

 

[tiny-tim]

welcome to pf!

hi wuid! welcome to pf!

(try using the X² button just above the Reply box )

let's see … that's a shelf of height a whose shape is a rectangle with a parabola cut out of it …

ok, you need it to have total probability of 1 ​

 

[wuid]

hi !
thx for the quick reply ,

let's see if i got u ,

$\int^{1}_{-1}\int^{1}_{u^{2}}advdu=1$

so $a=\frac{3}{4}$

is that right ?

 

[tiny-tim]

looks good!

 

[wuid]

can you please guide me with two more section in this problem ,
related to marginal functions & covariance ?

and i'll leave you for good :)

i

 

[tiny-tim]

i'm not much good at statistics

can you start a new thread? ​

 

[wuid]

o.k i'll start a new one later.

first i'll try harder... :)