## 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)?

1. yashar806

can you help?

2. yashar806

3. 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.

4. yashar806

i cant solve that euqation?

5. kropot72

6. yashar806

yep

7. kropot72

$4p ^{3}-4p ^{4}=p ^{4}$ First add 4p^4 to both sides.

8. yashar806

yep

9. kropot72

What did you get?

10. yashar806

4p^3= 5p^4

11. kropot72

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

12. yashar806

i dont get it

13. kropot72

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

14. yashar806

4/5?

15. kropot72

Yes, p = 4/5.

16. yashar806

17. 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?

18. yashar806

yes i did

19. yashar806

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

20. yashar806

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

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

ok

23. yashar806

could you explain that one please

24. kropot72

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