Firstly, I'm sorry if I'm posting an advanced question in the basic section, but I'm pretty sure this belongs here.
I took stats a few years ago and my course right now doesn't have a textbook so I'm not sure exactly how this is done.
Question reads: "The random variable X takes on one of the values 1,2,3,4,5 with probabilities
P(X=i) = ki, i = 1,2,3,4,5
for some value k. Find P(2 <= X <= 3)."
I'm not looking for a straight answer, just a question of where to start. I'm not sure but I thought that the sum of all P(X) across the domain of X (here [1,5]) should equal 1. So technically I should be able to solve for k right?
P(X) = kx
P(1) + P(2) + P(3) + P(4) + P(5) = 1.0
k + 2k + 3k + 4k + 5k = 1.0
14k = 1.0
k = 1/14
P(X) = x/14
In which case the probability that X is 2 or 3 should be:
P(2 <= X <= 3) = P(2) + P(3) = 2/14 + 3/14 = 5/14
Is that right? or am I doing something entirely different?