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Question:

Assume 2 treatments, 1 and 0. Given 120 participants, generate underlying truth with

  • Age as a discrete uniform distribution over integers between [20-60]
  • Gender (G) as $I\{G = F\} \sim \text{Bernoulli}(0.5)$
  • Potential outcomes matrix
    • $Y_i(0) \sim \text{Poisson}(5)$, $Y_i(1) \sim \text{Poisson}(10)$ for Female, and
    • $Y_i(0) \sim \text{Poisson}(6)$, $Y_i(1) \sim \text{Poisson}(6)$ for Male.

a. Find the causal effect for males and females respectively.

b. Generate the sampling distributions of $Pr(\text{Female} | Z=1)$, using 10,000 i.i.d. allocation vectors under: Coin toss with $Pr(\text{Treatment}) = 2/3$.

I've calculated the causal effect using the distributions mentioned in the question. However, I do not know what it means by the generating sampling distribution using coin toss with $Pr(\text{Treatment})$. Please advise or provide hints for me. Thanks

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  • 1
    $\begingroup$ "coin toss" means the binomial distribution. $\endgroup$ – Roland Sep 9 at 8:05

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