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M

  • 5 years ago

minerals produced from mines 1, 2, 3 and are independent normal random variables with means 80, 90, 75 pounds, respectively. what is the probability that the combined amount of mineral produced from all three mines exceeds 283 pounds? [Hint: use sum random variable Y = X1 + X2 + X3

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  1. anonymous
    • 5 years ago
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    0%. Even if you get 3 of the heaviest mineral, it only gives you 270 lbs (unless you means something else)

  2. M
    • 5 years ago
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    answer is .0351 you may need to use linear combinations

  3. anonymous
    • 5 years ago
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    What would be the constant? To you take out 1 mineral/mine or what?

  4. anonymous
    • 5 years ago
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    I think some info is missing.

  5. M
    • 5 years ago
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    no other information is given sorry

  6. M
    • 5 years ago
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    standard deviations 12, 14, 10 forgot crucial information!

  7. anonymous
    • 5 years ago
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    I got .036 do you know about moment generating functions?

  8. M
    • 5 years ago
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    some what the e^tx thing?

  9. anonymous
    • 5 years ago
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    yes it's the expected value of e^tx. Do you know the moment generating function for a normal random variable?

  10. M
    • 5 years ago
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    no but i can look it up

  11. anonymous
    • 5 years ago
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    i can type it for you... \[M(t)=e^{\mu*t+\sigma^{2}t^{2}/2}\]

  12. M
    • 5 years ago
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    there's so many variations of formulas i can't retain them in my memory

  13. anonymous
    • 5 years ago
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    that has mu as the mean and sigma as the standard deviation

  14. M
    • 5 years ago
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    i've seen that before but didn't actually had to solve any questions with it so far

  15. M
    • 5 years ago
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    do i use that formula?

  16. anonymous
    • 5 years ago
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    you use it to derive something that is helpful to remember about sum of independent normal vars. Do you want me to derive the result or just tell you what it is?

  17. M
    • 5 years ago
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    you can just tell me what it is lol

  18. anonymous
    • 5 years ago
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    ok haha. The mean of the sum of independent normal vars is the sum of the means, and the variance is the sum of the variances. So we have mean 80+90+75=245 and variance = 144+196+100=440

  19. anonymous
    • 5 years ago
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    then you convert it to standard normal and find the probability of being greater than 283 by looking a a standard normal chart

  20. anonymous
    • 5 years ago
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    do you know how to convert it?

  21. M
    • 5 years ago
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    what is standard normal? and i don't think we can use standard normal chart for this

  22. anonymous
    • 5 years ago
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    standard normal is normal with mean 0 variance 1. Well if you can't use the chart you just integrate. Do you know the pdf for normal variables?

  23. M
    • 5 years ago
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    yeah

  24. anonymous
    • 5 years ago
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    ok so you have the variance and mean, so you know the pdf and you integrate from 283 to infinity

  25. M
    • 5 years ago
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    i use the standard pdf formula?

  26. anonymous
    • 5 years ago
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    yes you can use that. It's kind of a mess though I usually use standard normal

  27. anonymous
    • 5 years ago
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    im looking at the integral now its pretty bad. I think I'd have to do it numerically. You haven't used standard normal in your class before?

  28. M
    • 5 years ago
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    hmm ok i'll have to play around with it for a while

  29. M
    • 5 years ago
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    no we've only used charts for z-score

  30. M
    • 5 years ago
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    everything else we just integrated or didn't use charts

  31. anonymous
    • 5 years ago
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    yeah z score, thats standard normal

  32. M
    • 5 years ago
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    oh haha

  33. anonymous
    • 5 years ago
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    you have mean and standard deviation so use the z score to find probability

  34. M
    • 5 years ago
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    i only knew it as table VI on pg 382 lol

  35. anonymous
    • 5 years ago
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    haha

  36. M
    • 5 years ago
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    using the z = (x-m)/st.dev?

  37. anonymous
    • 5 years ago
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    yeah that's it. stddev is sqrt( sum of the variances of each variable) mean is sum of the means

  38. M
    • 5 years ago
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    oh ok thanks. are you an actuary?

  39. anonymous
    • 5 years ago
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    im a graduate student in math studying modern algebra. I just took a grad probability class last semester though.

  40. M
    • 5 years ago
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    ahh nice

  41. anonymous
    • 5 years ago
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    are you in college?

  42. M
    • 5 years ago
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    no i graduated recently but taking some courses at local college

  43. M
    • 5 years ago
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    need it for grad school

  44. anonymous
    • 5 years ago
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    are you taking a prob/stats class now? i noticed a bunch of your questions are from that topic

  45. M
    • 5 years ago
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    probability and stat is worse than multivariable calc for me

  46. M
    • 5 years ago
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    yeah

  47. anonymous
    • 5 years ago
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    i like prob not stats. Did my answers to your other questions show up? Im not sure it worked.

  48. M
    • 5 years ago
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    yeah they did thanks. but haven't worked on them

  49. M
    • 5 years ago
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    but i have a good idea on how to solve them now though

  50. anonymous
    • 5 years ago
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    good. well ill cya around the site I just found it and I think its fun. good luck with your probability.

  51. M
    • 5 years ago
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    thanks!!

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