Probability & Statistics/Statistics



I just want to have a hint on how to start this items.

find the constant c so that p(x) satisfies the condition of being a probability density function of a random variable X:
I. p(x) = c(2/3)^x, x ∈ N
II. p(x) = cx, x ∈ {1,2,3,4,5,6}

Ive been trying to figure this for a couple of days. Thank you

In order for these to be valid probability density functions, their sum must be 1.

I. ∑ p(x) = ∑c(2/3)^x = c ∑(2/3)^x = c * 1 / (1-2/3) = 3c

This means c=1/3.

I am assuming N includes zero. Otherwise:

∑ p(x) = ∑c(2/3)^x = c ∑(2/3)^x = c * (2/3) / (1-2/3) = 2c, so c=2.

II. &sump; p(x) = c(1+2+3+4+5+6) = 21c

This means c=1/21.

This are really basic problems, and they are clearly homework. I know you want help, but you shouldn't come to the internet for help. I've given you the solution, but you need to learn from this. Please consult your course instructor for help on this material.

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Clyde Oliver


I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.


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