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yashar806

  • 2 years ago

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)?

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  1. yashar806
    • 2 years ago
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    can you help?

  2. yashar806
    • 2 years ago
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    please help

  3. kropot72
    • 2 years ago
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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.

  4. yashar806
    • 2 years ago
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    i cant solve that euqation?

  5. kropot72
    • 2 years ago
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    Do you want me to help you to solve the equation?

  6. yashar806
    • 2 years ago
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    yep

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

  8. yashar806
    • 2 years ago
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    yep

  9. kropot72
    • 2 years ago
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    What did you get?

  10. yashar806
    • 2 years ago
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    4p^3= 5p^4

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

  12. yashar806
    • 2 years ago
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    i dont get it

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

  14. yashar806
    • 2 years ago
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    4/5?

  15. kropot72
    • 2 years ago
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    Yes, p = 4/5.

  16. yashar806
    • 2 years ago
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    but the answer is 3/4

  17. kropot72
    • 2 years ago
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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?

  18. yashar806
    • 2 years ago
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    yes i did

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

  20. yashar806
    • 2 years ago
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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

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

  22. yashar806
    • 2 years ago
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    ok

  23. yashar806
    • 2 years ago
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    could you explain that one please

  24. kropot72
    • 2 years ago
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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.

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