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hmm.. i am working on a homework problem, and im kina stuck.

the question reads: Suppose that X is a random variable which can take on any non-negative integer (including 0). Write P(X greater than and equal to i) in terms of the probability mass function of X and hence show that

E[X] = the sum of infinity, i = 1 P(X greater than and equal to i)

I tried to solve this problem by just exanding it i times.

For example, i suppose i = 0, 1, 2, 3, 4 .....

So the probability mass funtion would look like:

P(1) = P{X = 1}

P(2) = P{X = 2}

P(3) = P{X = 3}

P(4) = P{X = 4}

i times.. etc.

but getting E[X] has got be completely lost

I thought perhaps that E[X] = 1P(X = 1) + 2P(X = 2) + 3P(X = 3) ..... but what are the values of the mass function?

Anybody have an idea?

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# Random variable

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