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Sir,

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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Comment | Thank you Sir. This means so much. Ill just use this as my guide to other given questions. Very much appreciated. |

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