Question

The following table shows the probability distribution for a discrete random variable.

X 24 26 27 32 35 39
P(X) 0.16 0.09 0.18 0.12 0.24 0.21
What is the mean of this discrete random variable? That is, what is E(X), the expected value of X?

A. 30.5
B. 31.47
C. 32.63
D. 29.5

Answer 1

\[E(x)=\sum_{i=1}^{N} x_iP(x_i)\]

Answer 2

in other words, mutliply each X by its P(X), and add all the results together

Answer 3

@amistre64

From where did you get this formula, and what do you mean when you say E(x)?

Answer 4

E(x) is the expected value ... which is just the average, or mean, of the expectations

Answer 5

spose for a game, you have 30% chance of winning 5 dollars, and have a 70% chance of losing 2 dollars

the expected value of playing the game is then: 5(.3)-2(.7) = 1.5-1.4 = 10 cents on average

Answer 6

10 cents what? Wining 10 cents or loosing 10 cents? Thanks for the explanation.

Answer 7

but thats not one of the multiple choices

Answer 8

your expected winnings over the course of many games is ... 10 cents per game

that doesnt mean you will win OR lose .. but that is what your overall expectations at playing multiple games would turn out to be

http://statistics.about.com/od/ProbHelpandTutorials/a/What-Is-The-Expected-Value.htm

Answer 9

can you put the e(x) furmula in steps plz

Answer 10

i did ... multiply each X by its P(X) and add up the results :/

Answer 11

Oh okay, so you are expected to win 10 cents in each game?

Answer 12

on average yes

Answer 13

Oh okay thanks a lot.

Answer 14

huh that link has nothing to do with my question

Answer 15

yes, it does. it gives the same steps as I have mentioned to you.

Answer 16

well im confused though can you do it in steps for me then

Answer 17

X 24 26 27 32 35 39
P(X) 0.16 0.09 0.18 0.12 0.24 0.21

what is 24 times .16 ?
what is 26 times .09 ?
what is 27 times .18 ?
what is 32 times .12 ?
... etc

after youve multiplied all the Xs with their P(X)s ... add em up

E(x) = 24(.16) + 26(.09) + 27(.18)+ ...

Answer 18

ok i get it now thx

Answer 19

youre welcome