Question

Find the constant c so that a random variable X is defined by taking on values 1 , 2 , … , n , … with probabilities c*(3/5)^n

Answer 1

I was thinking \[\frac{3}{5} = 1\] for the constant
so
\[1-\frac{3}{5} = \frac{2}{5}\]

\[\frac{\frac{3}{5}}{\frac{2}{5}} = \frac{3}{2}\]

Answer 2

is \[\frac{3}{2}= 1\]
\[c=\frac{2}{3}\]?

Answer 3

is my solution correct ?