Question

统计概率的问题~

The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a
new formula (formula B) with that of the standard formula (formula A). Each of three
judges is given three glasses in random order, two containing formula A and the other
containing formula B. Each judge is asked to state which glass he most enjoyed.
Suppose that two formulas are equally attractive. Let X be the number of judges
stating a preference for the new formula（A).

1. list all the elements of the sample space (S).
2. Find the probability distribution for a random variable X.
3. What is the probability that at least two of the judges state a preference for a
formula A?
4. Find the expected value of a random variable X.
5. Find the standard deviation of a random variable X.

Answer 1

1. list all the elements of the sample space (S).

S={0,1,2,3}

2. Find the probability distribution for a random variable X.

X服从n=3,p=1/2的二项分布，即B(3,1/2),分布律为
P(X=k)=C(3,k)*(1/2)^3=C(3,k)/8
所以
P(X=0)=C(3,0)*(1/2)^3=1/8
P(X=1)=C(3,1)*(1/2)^3=3/8
P(X=2)=C(3,2)*(1/2)^3=3/8
P(X=3)=C(3,2)*(1/2)^3=1/8

3. What is the probability that at least two of the judges state a preference for a formula A?

P(X>=2)=P(X=2)+P(X=3)=1/2

4. Find the expected value of a random variable X.

EX=np=3*1/2=3/2

5. Find the standard deviation of a random variable X

DX=np(1-p)=3/4

解毕

Answer 2

概率or统计?看看这是什么神奇的游戏?