## yashar806 Group Title 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 one year ago

1. yashar806 Group Title

can you help?

2. yashar806 Group Title

3. kropot72 Group Title

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

4. yashar806 Group Title

i cant solve that euqation?

5. kropot72 Group Title

6. yashar806 Group Title

yep

7. kropot72 Group Title

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

8. yashar806 Group Title

yep

9. kropot72 Group Title

What did you get?

10. yashar806 Group Title

4p^3= 5p^4

11. kropot72 Group Title

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

12. yashar806 Group Title

i dont get it

13. kropot72 Group Title

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

14. yashar806 Group Title

4/5?

15. kropot72 Group Title

Yes, p = 4/5.

16. yashar806 Group Title

17. kropot72 Group Title

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 Group Title

yes i did

19. yashar806 Group Title

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

20. yashar806 Group Title

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 Group Title

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 Group Title

ok

23. yashar806 Group Title

could you explain that one please

24. kropot72 Group Title

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