Respuesta :
Let X be the length of a randomly chosen scarf. To find the expected value of X, we should first recall how to calculate the expected value.
When X can take only a discrete set of values, the expected value of X is calculated as follows
[tex]E(X)\text{ = }\sum ^{}_{}xP(X=x)[/tex]this formula means that we should multiply each possible value for x with the probability of having that value, and then adding all values together.
So, for example, one term of this sum in this case would be
[tex]108\cdot P(X=108)[/tex]to calculate the term of the probability, we simply count how many scarfs we have of that length and divide it by the total amount of scarfs. So, we have 3 scarfs of length 108 and a total amount of 20 scarfs, so we have
[tex]P(X=108)=\frac{3}{20}[/tex]so, the first term would be
[tex]108\cdot\frac{3}{20}=16.2[/tex]We can fill the following table using the principles explained above
x # of scarfs P(X=x) x*P(X=x)
108 3 0.15 16.2
155
