# Expectation

• Dec 1st 2009, 03:25 PM
thomas_donald
Expectation
I am wondering if I could get help on the following HW problem:
3 trails each have the same probability of success. If X is the total # of successes and if E[X]=1.8. What is the smallest possible value of P(X=3)?
I know that the answer is 0 but I do not know why. I'll appreciate any help.
• Dec 1st 2009, 04:07 PM
ANDS!
Can you post the exact question?
• Dec 1st 2009, 11:32 PM
CaptainBlack
Quote:

Originally Posted by thomas_donald
I am wondering if I could get help on the following HW problem:
3 trails each have the same probability of success. If X is the total # of successes and if E[X]=1.8. What is the smallest possible value of P(X=3)?
I know that the answer is 0 but I do not know why. I'll appreciate any help.

Let \$\displaystyle p\$ be the probability of success on a single trial. Then:

\$\displaystyle E(X)=0.P(x=0)+1.P(x=1)+2.P(x=2)+3.P(x=3)=1.8\ \ \ \ ...(1)\$

where:

\$\displaystyle P(x=0)=(1-p)^3\$,

\$\displaystyle
P(x=1)=3.(1-p)^2.p
\$,

\$\displaystyle
P(x=2)=3.(1-p).p^2
\$,

\$\displaystyle
P(x=3)=p^3
\$.

Substituting these into the equation \$\displaystyle (1)\$ gives a cubic in \$\displaystyle p\$ and the question wants to know the smallest positive root of this cubic.

CB
• Dec 2nd 2009, 08:18 AM
thomas_donald
Thanks a lot for the help.
This is the exact question and the trails are not independent.