px(1 - p)n-x. Let X ~ Bin(10,0.25).
a.) Find P(X = 4).
0.1457
b.) Explain what a.) means in words (plain english).
If Bin(10,0.25) was our distribution, then the probability of four successes would be approximately 14.57%.
c.) Find P(X ? 2).
0.7563
d.) What is the mean and variance of this distribution?
Mean = 2.5
Variance = 1.875
2.) Let�s draw a tree diagram. Pretend that we went to a party and that thirty percent of the people are male. Then, of the males, ten percent are married. Of the females, twenty percent are single. Pretend also that there are single and married, male and female, only.
a.) Draw a tree diagram to represent the above situation.
Some tree diagram.
b.) What is the probability that someone is single?
0.41
c.) Of the people that are married, what is the probability that someone is female?
0.949
d.) Of the people that are male, what is the probability that someone is single?
0.90
3.) Let S= {a,b,d,e,g,h,1,2,7,8}. Let A={1,2,a,b,d} and let B= {a,b,d,e,g,h}.
a.) What is A U B?
{1,2,a,b,d,e,g,h}
b.) What about A ? B?
{a,b,d}
c.) What is A ? �?
{�}
d.) What is (� U S) ? A?
= A
4.) Let X be distributed as follows:
X 1 3 5 7
P(x) 0.15 0.25 0.55 0.05
a.) Find E(X).
4
b.) Find the standard deviation of X, St Dev(X). {Hint: Var(X) = E(X2) � (E(X))2}
Var(X) = 18.6 � 16 = 2.6
Std Dev(X) = 1.61