Let the random variable X ~ U ( 0, k ) and Y is a second random variable such as
Y | X ~ N ( X , 1).
a) Determine the Y density function if k = A .
b) Determine the value of k if COV [X , Y ] = B.
a)
So I started with this:
The density function of a uniform distribution is f(x)=1/(b-a), which is here f(x)=1/(k-0)
So we have f(x)=1/A
The density function of a normal distribution is in attachment ( because its hard to right here, the variables are associated like this ...~N(µ,, σ^2) )
The thing that i don't understand is how can the random variable X be in the arguments of the normal distribution, I'm used to have just a number and fill the numbers in the equation. And second thing, I don't really get the conditional transformation.
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