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anonymous

  • 5 years ago

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?

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  1. anonymous
    • 5 years ago
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    pls try

  2. amistre64
    • 5 years ago
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    for a population\[Var=\frac{\sum (x-X)^2}{n}\] hmmm

  3. anonymous
    • 5 years ago
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    ya......

  4. amistre64
    • 5 years ago
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    thats all I can come up with at the moment :/

  5. amistre64
    • 5 years ago
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    what does it mean: the mean of x^2 = 9?

  6. anonymous
    • 5 years ago
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    hey try the options for the ques are-80,20,144,112

  7. anonymous
    • 5 years ago
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    x square

  8. amistre64
    • 5 years ago
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    i know that much :) i just dont know what the sentence itself means

  9. anonymous
    • 5 years ago
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    oh,pls try

  10. amistre64
    • 5 years ago
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    if we add up all the x^2s and divide by how many there are we get 9 perhaps?

  11. amistre64
    • 5 years ago
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    (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

  12. anonymous
    • 5 years ago
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    hey how did u get this?

  13. amistre64
    • 5 years ago
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    i expanded the (x-X)^2 and split the fraction

  14. amistre64
    • 5 years ago
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    now, I believe the sum of x^2/n is the mean of x^2

  15. amistre64
    • 5 years ago
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    \[Var=\frac{\sum x^2}{n}-\frac{\sum 2xX}{n}+\frac{\sum X^2}{n}\] \[Var=9-\frac{\sum 2x(2)}{n}+\frac{\sum (2)^2}{n}\] \[Var=9-\frac{\sum 4x}{n}+4\] \[Var=13-\frac{\sum 4x}{n}\] is what im guessing so far

  16. amistre64
    • 5 years ago
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    now, \[\sum_{1}^{n} 4x=4\sum_{1}^{n}x=4(x_1+x_2+x_3+...+x_n)=4xn\]

  17. amistre64
    • 5 years ago
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    thats wrong; \[4\sum_{1}^{n} x=\frac{4n(n+1)}{2}=2n(n+1)\]

  18. amistre64
    • 5 years ago
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    divided by n = 2n+2 var = 13 - 2n + 2 var = 15 - 2n but that doesnt seem to be applicable as an answer tho

  19. amistre64
    • 5 years ago
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    well, class is starting so I gots to go; good luck :)

  20. anonymous
    • 5 years ago
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    ok..try afterward

  21. amistre64
    • 5 years ago
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    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 :) \[9-4\frac{\sum(x)}{n}+4\]

  22. amistre64
    • 5 years ago
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    i dont know why the last part is tacked on the end .... but its just spurious.

  23. anonymous
    • 5 years ago
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    ya thats what i did

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