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# Statistics help please: Linear Combinations of Random Variable

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1. The independent variables X and Y are such that X~B(10,0.8) and Y~Po(3). Find P(2X - Y =18).
I have tried to calculate the mean and variance of the combined variables but then realized that there is not much I can do with them since the final distribution is not a normal distribution. Please advise.
2. (Original post by VTan)
The independent variables X and Y are such that X~B(10,0.8) and Y~Po(3). Find P(2X - Y =18).
I have tried to calculate the mean and variance of the combined variables but then realized that there is not much I can do with them since the final distribution is not a normal distribution. Please advise.
Have you covered the convolution formula for the sum of two discrete random variables in your course? This gives you, if ,

Now adapt the proof of this to the sum and do the resulting calculation.
3. (Original post by Gregorius)
Have you covered the convolution formula for the sum of two discrete random variables in your course? This gives you, if ,

Now adapt the proof of this to the sum and do the resulting calculation.
I don't think that's under the CIE syllabus exam board. I haven't seen that formula before. It's alright, I'll try to read up on it and see how it works. Thank you for the help! =)
4. (Original post by VTan)
I don't think that's under the CIE syllabus exam board. I haven't seen that formula before. It's alright, I'll try to read up on it and see how it works. Thank you for the help! =)

Ah! Is this at "A" level? Then we can probably get away with something less heavy. You're told that X is binomial with a range of values from 0 to 10. Y is Poisson with a range of values from zero upwards. You want the value of P(Z = 2X - Y = 18). What values of X and Y will give you Z = 18? There are two possibilities and they are independent.

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