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Let $Y = a_1X_1 + a_2X_2 + a_3X_3 +....a_nX_n$, where $a_i $ are just constants and $X_i$ are independent Bernoulli random variables with probability of 0.5. Then what would be the distribution of Y? Thanks!

Tianyu Wang
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  • What do you want to know exactly? Its CDF, PDF, characteristic function or if it's a known distribution? – Harnak Jan 30 '19 at 09:15
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    If $n$ is large, you can approximate it with a Normal distribution. – Damien Jan 30 '19 at 09:17
  • Harnak: I want to know the pmf, especially the derivative of pmf near the mean value of Y. Damien: is this because of the CLT? – Tianyu Wang Jan 30 '19 at 09:45
  • Yes, because of the CLT. Note: when you address a comment to someone, don't forget to provide their name . @Harnak did not receive an alert about your comment to him – Damien Jan 30 '19 at 10:02
  • You get a discrete distribution. Difficult to define a derivative of the pmf, except if you use a non discrete (Normal) approximation – Damien Jan 30 '19 at 10:10

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