Find constant k with the probability mass function of a geometric series. f(x)=k(1/5)^{2x+3} where a discrete random variable X=0, 1, 2, 3,....

traucaderx7

traucaderx7

Open question

2022-08-14

Find constant k with the probability mass function of a geometric series
Ok so I'm having some trouble getting this done. I think I've got the answer but I'm not really sure on how I could verify that the result I got is actually the correct answer.
So here's what the exercise says:
f ( x ) = k ( 1 5 ) 2 x + 3
where a discrete random variable X = 0 , 1 , 2 , 3 , . . . .
So I know this is a function for a geometric series given that the range for X is infinite.
Here's what I did:
1. i = 0 k ( 1 5 ) 2 x + 3 = 1
2. k 125 i = 0 ( 1 5 ) 2 x = 1
3. k 125 ( 1 1 1 5 ) = 1
4. k 125 ( 5 4 ) = 1
5. k 100 = 1
6. k = 100
So how do I know that is ok, I thought about using limits but I'm not sure if that is correct.

Answer & Explanation

Payton Mcbride

Payton Mcbride

Beginner2022-08-15Added 18 answers

Explanation:
Observe
X = 0 k ( 1 5 ) 2 X + 3 = k 125 X = 0 ( 1 5 ) 2 X = k 125 X = 0 ( 1 25 ) X = k 125 1 1 1 25

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