Describe two way of finding the expected value?

Question

Question 1: 18% of high school boys and 10% of high school girls say they rarely or never wear seat belts. Suppose one high school boy and one high school girl are selected at random, with the random variable of interest being the number in the pair who say they rarely or never wear seat belts. Describe two ways of finding the expected value and standard deviation of this random variable, at least approximately.

Answer 1

(1) If you let the random variable x=how many of the two people wear a seat belt then x=0,1,2.

 

     Find the probability distribution p(x) of x and calculate Σxp(x)=expected value

 

(2) If x is the random variable of the boy and y for the girl then x=0 or 1 and y=0 or 1,

 

      Exp(x + y)=E(x) + E(y)

 

These of course are the "descriptions" of two ways. There's more math involved to get the answers (which must be the same.)

 

Shelby: If you need more detail for this question feel free to go to my profile and send me a message. I teach classes in statistics and probability.