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 one year 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)?
 one year 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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kropot72
 one year ago
Best ResponseYou've already chosen the best response.0\[P(X=3)=\left(\begin{matrix}4 \\ 3\end{matrix}\right)p ^{3}(1p)=4p ^{3}(1p)=4p ^{3}4p ^{4}\] \[P(X=4)=\left(\begin{matrix}4 \\ 4\end{matrix}\right)p ^{4}(1p)^{0}=p ^{4}\] \[4p ^{3}4p ^{4}=p ^{4}\ ....................(1)\] Now solve equation (1) to find the value of p.

yashar806
 one year ago
Best ResponseYou've already chosen the best response.0i cant solve that euqation?

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0Do you want me to help you to solve the equation?

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0\[4p ^{3}4p ^{4}=p ^{4}\] First add 4p^4 to both sides.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0Now divide both sides by 5p^3 and post the result.

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{4p ^{3}}{5p ^{3}}=\frac{5p ^{4}}{5p ^{3}}\] Now simplify.

yashar806
 one year ago
Best ResponseYou've already chosen the best response.0but the answer is 3/4

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0If 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?

yashar806
 one year ago
Best ResponseYou've already chosen the best response.0anyway, i gotthe idea, can I ask you one more question, i just need an explanation, please

yashar806
 one year ago
Best ResponseYou've already chosen the best response.0A 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
 one year ago
Best ResponseYou've already chosen the best response.0Here is the checking of the answer p = 4/5: \[P(X=3)=\left(\begin{matrix}4 \\ 3\end{matrix}\right)\times (\frac{4}{5})^{3}\times \frac{1}{5}=(\frac{4}{5})^{4}\] \[P(X=4)=\left(\begin{matrix}4 \\ 4\end{matrix}\right)\times (\frac{4}{5})^{4}\times (\frac{1}{5})^{0}=(\frac{4}{5})^{4}\]

yashar806
 one year ago
Best ResponseYou've already chosen the best response.0could you explain that one please

kropot72
 one year ago
Best ResponseYou've already chosen the best response.0@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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