Consider two random variables X,Y whose correlation is ρ = 0.7 (and the joint PMF is football shaped). Predict the z-score for Y if you observe that X is at the 30th percentile (assuming X ~ N(4,4)).
The solution to this problem is -0.364, but I'm not sure how to approach this answer.
If X ~ N(2,4) then Y = -X-1 is also a normal random variable such that Y ~ N(μ,σ^2).
Find μ and σ^2.
I know that E(X) = 2 and Var(X) = 4.
E(Y) = -E(X) - 1
E(Y) = -2 - 1 = -3
So I found μ, but I'm not sure how to find the variance. Help?
What is a countable set exactly? HELP? Can someone help guide me through this problem? I'm a bit lost on how to show this...
Countable union of countable sets: Let I be a countable set. Let Ai , i ∈ I be a family of sets such that each Ai is countable. We will show that U i ∈ I Ai is countable...