suppose that P(Yi=1)=1-P(Yi=0)=0.8,i=1,...,10, where Y1,...Y10 are independent. Let Y=Y1+...+Y10. Then the distribution of Y is Binomial...

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suppose that P(Yi=1)=1-P(Yi=0)=0.8,i=1,...,10, where Y1,...Y10 are independent. Let Y=Y1+...+Y10. Then the distribution of Y is Binomial...

suppose that P(Yi=1)=1-P(Yi=0)=0.8,i=1,...,10, where Y1,...Y10 are independent. Let Y=Y1+...+Y10. Then the distribution of Y is Binomial with mean 2.

Does the above statement correct and explain why? Thank you.

math Statistics-And-Probability

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Answer 1

Answer #1

Since Yi is a random variable taking two values namely 0 and 1 then the total probability should be 1. So P(Yi=1)=1-P(Yi=0)=0.8 is wrong. The total probability to be 1 then the corresponding probability should be P(Yi=1)=1-P(Yi=0)=0.5.

If P(Yi=1)=0.2 then your Explanation is correct

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Answer 2

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suppose that P(Yi=1)=1-P(Yi=0)=0.8,i=1,...,10, where Y1,...Y10 are independent. Let Y=Y1+...+Y10. Then the distribution of Y is Binomial...