Question

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

X 22 24 25 30 33 37
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. 27.5
B. 28.5
C. 29.47
D. 30.27

Answer 1

HI!!

Answer 2

boring exercise, you have to multiply and add

Answer 3

\[22\times .16+24\times .09+...\] all the way down the line

Answer 4

so we have an X vector, and P(X) vector, and we want the dotproduct ...

Answer 5

lol dot product !!

Answer 6

X 22 24 25 30 33 37
P(X) 0.16 0.09 0.18 0.12 0.24 0.21

out of 100, we expect

16 values of 22
9 values of 24
18 values of 25
12 values of 30
24 values of 33
21 values of 37

sum of all events =
+(22+22+...+22) ; 16 times
+(24+24+...+24) ; 9 times
+(25+25+...+25) ; 18 times
+(30+30+...+30) ; 12 times
+(33+33+...+33) ; 24 times
+(37+37+...+37) ; 21 times
-------------
n = 100 events

mean is defined as ... sum of all events, divided by the number of events.

Answer 7

or you could work with the decimals and not divide by 100 at the end right?

Answer 8

just making a point is all, showing how we go from the definition of a mean to the sum of xP(x)
\[\frac{22(16)+24(9)+25(18)+30(12)+33(24)+37(21)}{100}\]
\[22(\frac{16}{100})+24(\frac{9}{100})+25(\frac{18}{100})+30(\frac{12}{100})+33(\frac{24}{100})+37(\frac{21}{100})\]
\[22(.16)+24(.09)+25(.18)+30(.12)+33(.24)+37(2.1)\]

Answer 9

.21 on the end :)

Answer 10

so whats the answer?

Answer 11

you want us to add and multiply for you? nah, thats on you.

Answer 12

I was just confused...sorry. So, i add 22(.16)+24(.09)+25(.18)+30(.12)+33(.24)+37(2.1) all that and i multiply what?

Answer 13

when i added everything i got 99.4

Answer 14

lets see what the wolf gives us :) so we avoid any mistakes

Answer 15

.21, not 2.1


22(.16)+24(.09)+25(.18)+30(.12)+33(.24)+37(.21)
^^^^

http://www.wolframalpha.com/input/?i=22%28.16%29%2B24%28.09%29%2B25%28.18%29%2B30%28.12%29%2B33%28.24%29%2B37%28.21%29

29.47

Answer 16

ohhh okay thank you :-)

Answer 17

yep