Question 10.

Consider the following experiment; simultaneously toss a fair coin and independently roll a fair die

- Write out the 12 outcomes that comprise the sample space for this experiment.

The toss of the coin = (Head, tail)

Throw of the die = {1,2,3,4,5,6}

Combination of the two events ={(1 Head), (1Tail),…, (6Head), (6 Tail).

The probability of tossing a coin and getting a head or a tail would be equal that is =1/2

P(AB) = P(A)P(B) = ½ X1/2 =1/4

From the sample space of twelve, it can be deduced that 3 of the twelve likely events comprise AB, and that; P(AB) = P(A) + P(B) – P(AB) =3/4. That is nine of twelve equally likely events makes AB

- Let X be a random variable that takes the value of 1 if the coin shows heads and the value of 0 if the coin shows tails. Let Y be the random variable that takes the value of the up face of the tossed die. And let Z = X+Y. construct the probability mass function for Z

For independent variables

P_{XY} |
X1=-1 | X2 = 0 | X3 = 1 | P_{Y}(yj) |

Y1=-1 | 1/12 | 1/6 | 1/4 | 1/2 |

Y2=0 | 1/18 | 1/9 | 1/6 | 1/3 |

Y3=1 | 1/36 | 1/18 | 1/12 | 1/6 |

PX(Xk) | 1/6 | 1/3 | 1/2 |

For joint probability function

P) | X1=1 | X2 = 0 | P |

Y1=-1 | 1/12+1/4+1/36+1/12=4/9 | 1/6+1/18=2/9 | 2/3 |

Y2=0 | 1/18+1/6=2/9 | 1/9 | 1/3 |

P(Xk) | 2/3 | 1/3 |

- Find the mean of Z

- Find the variance for Z

Question 1

The number of customers entering a certain restaurant in any given day is approximately normally distributed with a mean of 40 and a standard deviation of 10. Find the probability that during a given day;

- At least 40 customers arrive P(X>=40) = 0.5
- No more than 45 customers arrive P(X=<45)

P(X

P(X 0.6915

Question 7.

- Calculation of the pooled estimate of the standard deviation

- Use the turkeys multiple comparison procedure to compare the mean rates of penetration for the three drill bits. Identify the means that differ. Use α=0.01.

This represents a 99% level of confidence.

For a two sided system the degree of freedom can be calculated from

0.99/2=0.495