Finding the Probability Mass Function for Y = 0,1,2,3...

[rad0786]

Y = 0 ... -e^(-1/8) +1
Y = 1 ... -e^(-3/8) + e^(-1/8)
Y = 2 ... -e^(-5/8) + e^(-3/8)
Y = 3 ... -e^(-7/8) + e^(-5/8)
Y = 4 ... -e^(-9/8) + e^(-7/8)

Y = y ... -e^-(y+0.5)/4 + e^-(y-0.5)/4 for y = 1,2,3...

See the above equation, that only works for y = 1,2,3... anybody know how i could make an equation that would include y = 0? so that y = 0,1,2,3...

This comes from a stats assignment asking to derive the probability mass function. I got this pattern out of it, i just cannot get zero into it. Anybody have any ideas?

 

[Nino MMP]

The equation can be modified to include y = 0 by subtracting 0.5 from the exponent instead of adding it. This gives the equation: Y = y ... -e^-(y-0.5)/4 + e^-(y-1.5)/4 for y = 0,1,2,3...