Expected value problem?

the random variable x represents the number of credit cards that adults have along with the corresponding probabilities (hint: n = 1.0)





X P(x)





0 .49


1 .05


2 .32


3 .07


4 .07





a) what is the expected value and standard deviation?


b)what is the probability of owning exactly two credit cards?


c) what is the probability of owning at least two c.c?


and is this empirical or classical probability?





ok, I am not asking for someone to give me the answers. I am asking HOW TO ACHIEVE the answers.


show me how to.........please. thank you

Expected value problem?
(A) The expected value is the sum over X of XP(x), or





0(.49) + 1(.05) + 2(.32) + 3 (.07) + 4 (.07) = 1.18 credit cards.





For standard deviation, we need a weighted average. (I have done it step-by-step for you here, but it is really not so long once you are practiced!) Standard deviation is given by the formula





sqrt(summation over X of [((X - E(X))^2)P(X)]) =





sqrt((0 - 1.18)^2(.49) + (1-1.18)^2(.05) + (2-1.18)^2(.32) +


(3-1.18)^2(.07) + (4-1.18)^2(.07) )=





{remember to begin with subtracting the stuff in parentheses, and then square it!}





sqrt((1.3924)(2.49) + (.0324)(.05) + ((.6724)(.32) + ((3.3124)(.07) + ((7.9524)(.07)} =





{now, remember to multiply next, and then add, and finally to take the square root}





sqrt (3.467076 + .00162 + .215168 + .231868 + .556668} =





sqrt{4.3624} = 2.088635918 = 2.09








(B) The probability of owning 2 credit cards is P(2)= .32, or 32%. from your table of X and P(x).





(C) P(owning at least two cc's) = P(2) + P(3) + P(4) = .46 = 46%





Finally, we need to interpret our results. Empirical probability is the same as relative frequency, namely the frequency as calculated from experimental data. Since we are told that the data given are probabilistic, it follows that all of our calculations must be taken as classical probability as well.





N.B.: If you take these data to be experimental, then the answer becomes "empirical probability".





Redo these problems, now that you know how, and see that you can get each part right! GOOD SKILL! : c )

phone cards