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yashar806

A random variable X has a binomial distribution with parameters n = 4 and p. What must be the value of the parameter p if we know that P(X = 3)= P(X = 4)?

  • one year ago
  • one year ago

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  1. yashar806
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    can you help?

    • one year ago
  2. yashar806
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    please help

    • one year ago
  3. kropot72
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    \[P(X=3)=\left(\begin{matrix}4 \\ 3\end{matrix}\right)p ^{3}(1-p)=4p ^{3}(1-p)=4p ^{3}-4p ^{4}\] \[P(X=4)=\left(\begin{matrix}4 \\ 4\end{matrix}\right)p ^{4}(1-p)^{0}=p ^{4}\] \[4p ^{3}-4p ^{4}=p ^{4}\ ....................(1)\] Now solve equation (1) to find the value of p.

    • one year ago
  4. yashar806
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    i cant solve that euqation?

    • one year ago
  5. kropot72
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    Do you want me to help you to solve the equation?

    • one year ago
  6. yashar806
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    yep

    • one year ago
  7. kropot72
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    \[4p ^{3}-4p ^{4}=p ^{4}\] First add 4p^4 to both sides.

    • one year ago
  8. yashar806
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    yep

    • one year ago
  9. kropot72
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    What did you get?

    • one year ago
  10. yashar806
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    4p^3= 5p^4

    • one year ago
  11. kropot72
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    Now divide both sides by 5p^3 and post the result.

    • one year ago
  12. yashar806
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    i dont get it

    • one year ago
  13. kropot72
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    \[\frac{4p ^{3}}{5p ^{3}}=\frac{5p ^{4}}{5p ^{3}}\] Now simplify.

    • one year ago
  14. yashar806
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    4/5?

    • one year ago
  15. kropot72
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    Yes, p = 4/5.

    • one year ago
  16. yashar806
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    but the answer is 3/4

    • one year ago
  17. kropot72
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    If you test the value of p = 3/4 you will find that it is not correct. Testing the value of p = 4/5 shows that it is correct. Did you copy the original question correctly?

    • one year ago
  18. yashar806
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    yes i did

    • one year ago
  19. yashar806
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    anyway, i gotthe idea, can I ask you one more question, i just need an explanation, please

    • one year ago
  20. yashar806
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    A variable X follows a normal distribution with mean 10 and standard deviation 5. Another variable Y follows a normal distribution with mean 25 and standard deviation 10. The maximum height of the density curve for X is_______ (i) the maximum height for the density curve for Y , and the area under the density curve for X is__________ (ii) the area under the density curve for Y . (A) (i) greater than, (ii) less than (B) (i) less than, (ii) greater than (C) (i) equal to, (ii) equal to (D) (i) greater than, (ii) equal to (E) (i) less than, (ii) less than

    • one year ago
  21. kropot72
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    Here is the checking of the answer p = 4/5: \[P(X=3)=\left(\begin{matrix}4 \\ 3\end{matrix}\right)\times (\frac{4}{5})^{3}\times \frac{1}{5}=(\frac{4}{5})^{4}\] \[P(X=4)=\left(\begin{matrix}4 \\ 4\end{matrix}\right)\times (\frac{4}{5})^{4}\times (\frac{1}{5})^{0}=(\frac{4}{5})^{4}\]

    • one year ago
  22. yashar806
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    ok

    • one year ago
  23. yashar806
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    could you explain that one please

    • one year ago
  24. kropot72
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    @yashar806 Please post your second question again after closing this one. Sorry I cannot help any further. I must log out now.

    • one year ago
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