Question

DO NOT FORGET THAT YOU ARE TO USE CHAPTER 6 MATERIAL FOR PROBLEMS 3 AND 4. NO CREDIT FOR USING PREVIOUS CHAPTER'S MATERIAL 3. (8 points) Team A has probability 0.3 of winning whenever it plays (and there are no ties). Let X denote the number of times Team A wins in five games. h) Find the distribution of X. i) Find the mean, variance and standard deviation of X. 4. (8 points) A box contains 4 white, 5 red and 2 blue marbles. A sample of six marbles is drawn with replacement. Find the probability that one is blue, two are white and three are red.

Answer 1

3. Givne n = 5 games, p = 0.3

h) The distribution of X is (using binomial distribution)

PfX =x)=:10.3x (1-0.3)5-x, x = 0,1,2, ,5

Clearly,

x	P(X=x)
0	0.16807
1	0.36015
2	0.3087
3	0.1323
4	0.02835
5	0.00243

h) Mean =np = 5*0.3 = 1.5

Variance = npq = 5*0.3*0.7 = 1.05

SD = 1.0247

4)

Total marbles = 4+5+2 = 11
The number of ways select from 6 marbles from 11 marbles is 11C₆ = 462
The number of ways select from 1 blue from 2 blue marbles is 2C₁ = 2
The number of ways select from 2 white from 4 white marbles is 4C₂ = 6
The number of ways select from 3 red from 5 red marbles is 5C₃ = 10

Required probability = 2*6*10 / 462 = 0.25974