(High school statistics) Expected value of a probability table

So I have a probability table with the values and their probabilities: $$\begin{array}{|l|l:l|} \hline X & 0 & 1 & 2 & 3 & 4\textsf{ or more} \\ \hdashline \mathsf P_{\!X} & 0.49 & 0.35 & 0.12 & 0.03 & 0.01 \\ \hline \end{array}$$ How would I find the expected value? I know you would take the probability and multiply it by the value and do this for all the values to find the expected value and that works for 1, 2 and 3, but I'm not sure what to do when it comes to '4 or more' because thats a range of values. What would I need to do to find the expected value?

Thanks.(Sorry about formatting, probabilities and what they align with go from left to right respectively (ed: it's now in a MathJax table for you))

• You cannot find the expected value with the given information. You can find a range of possible values for the expected value but not its exact value. – Jimmy R. Nov 18 '15 at 10:43

Indeed you do need to assign a single value to the last category so that you may evaluate an expected value.

Rather than the undefinable $\mathsf E(X)$ you may only sensibly discuss $\mathsf E(\min\{X, 4\})$ .

• Thanks for the edit, I appreciate that – BLAZE Nov 18 '15 at 11:03

Start like this:

Let $X$ be some random variable

$$\begin{array}{|c|l:l|}\hline x & \mathsf P(X=x) & x\,\mathsf P(X=x) \\ \hline 0 & 0.49 & 0.00 \\ 1 & 0.35 & 0.35 \\ 2 & 0.12 & 0.24 \\ 3 & 0.03 & 0.09 \\ \hdashline \gt 4 & 0.01 & >0.04 \\ \hline \end{array}$$

When it comes to four or more you need to specify a range or an upper limit

• I am not the downvoter. I think the downvote is linked to $0.04$ where $x>4$. Graham repaired it now. – drhab Nov 18 '15 at 10:59
• No, the downvote, was linked to to x=1, x=2, x=3, x=4, x>4 and not x=0, x=1, x=2 and so on... – Jimmy R. Nov 18 '15 at 11:00
• @Stef Yes that's it as I put 4 then >4 but OP asking for 4 or more my mistake misread it sorry – BLAZE Nov 18 '15 at 11:00
• @Stef $x=0$ can be looked at as irrelevant in this context of calculating expectation. – drhab Nov 18 '15 at 11:01
• @BLAZE No, problem I removed the downvote as soon as you corrected it! – Jimmy R. Nov 18 '15 at 11:03