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Let $Y_1, . . . , Y_n$ be a random sample from a zero-truncated Poisson distribution with probability mass function:

$p_Y (y|λ) = k\frac{λ^ye^{-y}}{y!},$
$k > 0, λ > 0, y = 1, 2, . . . ,$ where k is an unknown constant.

I know that the sum of a probability mass function is 1, but I do not know how to use this information to find $k$.

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    $\begingroup$ You need to sum the series. However, your formula for the pmf is wrong! $\endgroup$
    – Glen_b
    Commented Nov 21, 2017 at 23:50
  • $\begingroup$ My problem is that I don't know how to do this, but thank you for confirming what I had suspected! $\endgroup$
    – Clong123
    Commented Nov 21, 2017 at 23:53
  • $\begingroup$ See stats.stackexchange.com/search?q=truncated+poisson+distribution for more. $\endgroup$
    – whuber ♦
    Commented Nov 21, 2017 at 23:55
  • $\begingroup$ @Clong123 could you sum it if it wasn't truncated? $\endgroup$
    – Glen_b
    Commented Nov 22, 2017 at 0:58

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