Question

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)?

Answer 1

can you help?

Answer 2

please help

Answer 3

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

Answer 4

i cant solve that euqation?

Answer 5

Do you want me to help you to solve the equation?

Answer 6

yep

Answer 7

\[4p ^{3}-4p ^{4}=p ^{4}\]
First add 4p^4 to both sides.

Answer 8

yep

Answer 9

What did you get?

Answer 10

4p^3= 5p^4

Answer 11

Now divide both sides by 5p^3 and post the result.

Answer 12

i dont get it

Answer 13

\[\frac{4p ^{3}}{5p ^{3}}=\frac{5p ^{4}}{5p ^{3}}\]
Now simplify.

Answer 14

4/5?

Answer 15

Yes, p = 4/5.

Answer 16

but the answer is 3/4

Answer 17

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?

Answer 18

yes i did

Answer 19

anyway, i gotthe idea, can I ask you one more question, i just need an explanation, please

Answer 20

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

Answer 21

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

Answer 22

ok

Answer 23

could you explain that one please

Answer 24

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