Question

What is E(x), the expected number of bases for Ichiro at a typical at-bat in 2001?

During his 2001 MVP season for the Seattle Mariners, Japanese baseball sensation Ichiro Suzuki hit 190 singles, 32 doubles, 10 triples, and 10 home runs in a total of 692 at-bats. The following table arranges these data in terms of the number of bases for a hit, counting 0 bases for the times when he did not get a hit, and 4 bases for home runs.

Number of Bases 0 1 2 3 4
Number of Times 450 190 32 10 10

What was E(x), the expected number of bases for Ichiro at a typical at-bat in 2001

Answer 1

expected value is the value times the probability of that value occurring

in this case, the # of bases times the probability of getting that many bases in an at bat

the probability is a ratio. For example,
probability of a single base is # of singles divided by total number of at-bats

Answer 2

so would i do 450*0*190*1+32*2+10*3+10*4 and then divide that by 692?

Answer 3

yes, (assuming that 450*0*190*1 is a typo, and should be 450*0+190*1)

the 692 divides each "at-bat number", but you can factor it out, and divide at the end.

Answer 4

as a sanity check, the expected number of bases should be bigger than 0 and less than 4

Answer 5

yeah it was a typo
thanks so much
so if i do out the math it should be 81/173 which is .468208 which is bigger than 0 and less than 4.
thank you for all of your help!! :D