Question

random variable x s properties(i)the mean of X is 2. and (2) the mean of x^2 is 9.what is variance of 4x?

Answer 1

pls try

Answer 2

for a population\[Var=\frac{\sum (x-X)^2}{n}\]

hmmm

Answer 3

ya......

Answer 4

thats all I can come up with at the moment :/

Answer 5

what does it mean: the mean of x^2 = 9?

Answer 6

hey try the options for the ques are-80,20,144,112

Answer 7

x square

Answer 8

i know that much :) i just dont know what the sentence itself means

Answer 9

oh,pls try

Answer 10

if we add up all the x^2s and divide by how many there are we get 9 perhaps?

Answer 11

(x-X)^2 = x^2 -2xX + X^2

\[Var=\frac{\sum x^2}{n}-\frac{\sum 2xX}{n}+\frac{\sum X^2}{n}\]
might be useful if its correct

Answer 12

hey how did u get this?

Answer 13

i expanded the (x-X)^2 and split the fraction

Answer 14

now, I believe the sum of x^2/n is the mean of x^2

Answer 15

\[Var=\frac{\sum x^2}{n}-\frac{\sum 2xX}{n}+\frac{\sum X^2}{n}\]

\[Var=9-\frac{\sum 2x(2)}{n}+\frac{\sum (2)^2}{n}\]

\[Var=9-\frac{\sum 4x}{n}+4\]

\[Var=13-\frac{\sum 4x}{n}\]
is what im guessing so far

Answer 16

now, \[\sum_{1}^{n} 4x=4\sum_{1}^{n}x=4(x_1+x_2+x_3+...+x_n)=4xn\]

Answer 17

thats wrong;
\[4\sum_{1}^{n} x=\frac{4n(n+1)}{2}=2n(n+1)\]

Answer 18

divided by n = 2n+2

var = 13 - 2n + 2

var = 15 - 2n

but that doesnt seem to be applicable as an answer tho

Answer 19

well, class is starting so I gots to go; good luck :)

Answer 20

ok..try afterward

Answer 21

I want to say its 20.

to recap: a mean is an average, an average is adding up all the values and dividing by how many there are.
\[avg(x_1,x_2,x_3,...,x_n)=\frac{x_1+x_2+x_3+...+x_n}{n}=\frac{\sum x}{n}=\mu\]

given that:\[\mu=2;\ and\ \frac{\sum(x^2)}{n}=9\]what is variance of 4x?

From algebra we know that (x-u)^2 can be expanded to:

x^2 -2xu + u^2\[\frac{\sum (x-\mu)^2}{n}=\frac{\sum (x^2-2x\mu+\mu^2)}{n}=\frac{\sum(x^2)}{n}-\frac{\sum(2x\mu)}{n}+\frac{\sum(\mu^2)}{n}\]
replace this with known values:
\[9-\frac{\sum(2x*2)}{n}+\frac{\sum(2^2)}{n}\]
constants can be factored out and the average of a constant is itself
\[9-4\frac{\sum(x)}{n}+4\]
relpace known values
\[9-4*2+4=5\]
\[var(x)=5\]
we want to know the variance of 4 times x which I would say is 4*5 = 20

but i reserve the right to be complety wrong :)
\[9-4\frac{\sum(x)}{n}+4\]

Answer 22

i dont know why the last part is tacked on the end .... but its just spurious.

Answer 23

ya thats what i did