anonymous
  • anonymous
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)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
can you help?
anonymous
  • anonymous
please help
kropot72
  • kropot72
\[P(X=3)=\left(\begin{matrix}4 \\ 3\end{matrix}\right)p ^{3}(1-p)=4p ^{3}(1-p)=4p ^{3}-4p ^{4}\] \[P(X=4)=\left(\begin{matrix}4 \\ 4\end{matrix}\right)p ^{4}(1-p)^{0}=p ^{4}\] \[4p ^{3}-4p ^{4}=p ^{4}\ ....................(1)\] Now solve equation (1) to find the value of p.

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More answers

anonymous
  • anonymous
i cant solve that euqation?
kropot72
  • kropot72
Do you want me to help you to solve the equation?
anonymous
  • anonymous
yep
kropot72
  • kropot72
\[4p ^{3}-4p ^{4}=p ^{4}\] First add 4p^4 to both sides.
anonymous
  • anonymous
yep
kropot72
  • kropot72
What did you get?
anonymous
  • anonymous
4p^3= 5p^4
kropot72
  • kropot72
Now divide both sides by 5p^3 and post the result.
anonymous
  • anonymous
i dont get it
kropot72
  • kropot72
\[\frac{4p ^{3}}{5p ^{3}}=\frac{5p ^{4}}{5p ^{3}}\] Now simplify.
anonymous
  • anonymous
4/5?
kropot72
  • kropot72
Yes, p = 4/5.
anonymous
  • anonymous
but the answer is 3/4
kropot72
  • kropot72
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?
anonymous
  • anonymous
yes i did
anonymous
  • anonymous
anyway, i gotthe idea, can I ask you one more question, i just need an explanation, please
anonymous
  • anonymous
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
kropot72
  • kropot72
Here is the checking of the answer p = 4/5: \[P(X=3)=\left(\begin{matrix}4 \\ 3\end{matrix}\right)\times (\frac{4}{5})^{3}\times \frac{1}{5}=(\frac{4}{5})^{4}\] \[P(X=4)=\left(\begin{matrix}4 \\ 4\end{matrix}\right)\times (\frac{4}{5})^{4}\times (\frac{1}{5})^{0}=(\frac{4}{5})^{4}\]
anonymous
  • anonymous
ok
anonymous
  • anonymous
could you explain that one please
kropot72
  • kropot72
@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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