Suppose student Ana is running for a charity and asks her friend to chip in the donation. Suppose each friend donates independently, and the value Tᵢ is a random variable with the following probability density:
p(Tᵢ=tᵢ)= {c tᵢ∈[10,20] dollars
{c tᵢ ∈[40,50] dollars
{0 otherwise
Let's assume Tᵢ ′s are mutually independent and each donation is a continuous random variable given they're using electronic transfer. Ana requested from 100 friends for the donation. Let X be the total amount in dollar Ana collected from these 100 friends. You need to simplify for this problem.
Which of the following theorems or concepts are referenced in the entire question?
(a) Weak Law of Large Numbers
(b) i.i.d.
(c) Central Limit Theorem