# Thread: Discrete probability

1. ## Discrete probability

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
therefore:
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?

2. Hello,

Perfect reasoning

except that 1+2+3+4+5=15, not 14

3. Oops... You are of course correct Moo. I'm really surprised my logic isn't in some way flawed (even if my implementation is).

Thanks a lot!

4. Originally Posted by sadmath
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
therefore:
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
You have a small error. $k=\frac{1}{\color{blue}15}$

5. Thanks for the reply Plato, but I think Moo beat you to the punch

6. Originally Posted by sadmath
Thanks for the reply Plato, but I think Moo beat you to the punch
She beats most people to the punch (she's that kind of cow).

7. Originally Posted by mr fantastic
She beats most people to the punch (she's that kind of cow).
I prefer beating people to (drinking) ponch