Find constant k with the probability mass function of a geometric seriesOk 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 = 12. k 125 ∑ i = 0 ∞ ( 1 5 ) 2 x = 13. k 125 ( 1 1 − 1 5 ) = 14. k 125 ( 5 4 ) = 15. k 100 = 16. k = 100So how do I know that is ok, I thought about using limits but I'm not sure if that is correct.

Question

Find constant k with the probability mass function of a geometric seriesOk so I&#039;m having some trouble getting this done. I think I&#039;ve got the answer but I&#039;m not really sure on how I could verify that the result I got is actually the correct answer.So here&#039;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&#039;s what I did:1.       ∑          i      =      0        ∞    k  (      1    5        )          2      x      +      3        =  12.       k    125        ∑          i      =      0        ∞    (      1    5        )          2      x        =  13.       k    125    (      1          1      −              1        5              )  =  14.       k    125    (      5    4    )  =  15.       k    100    =  16.   k  =  100So how do I know that is ok, I thought about using limits but I&#039;m not sure if that is correct.

Payton Mcbride · Accepted Answer

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

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,....

Open question

Answer & Explanation

New Questions in High school geometry