Question

1. T F The number of defects on a product produced by a process is distributed as a Poisson distribution.

2. T F For large binomially distributed populations and small samples you can use sampling without replacement

3. T F Given a triangular distribution with minimum 2, maximum 8 and mode 7, the probability of being smaller than 7 is greater than 60%

4. T F The hypergeometric distribution describes sampling without replacement

5. T F The relative frequency of a value is the proportion of times the value occurs.

6. T F The permutation of n numbers is always smaller than the combination of the same n numbers, taken the same number of times

7. T F The intersection of two events is greater than zero when they are mutually exclusive

8. T F The probability of rolling a 6 with a fair six sided die is 1/6.

9. T F The product of the probability of two independent events is called conditional probability.

10. T F When we use both a beta and a triangular distribution to represent a variable, the probability of a low value will always be grater with the triangular distribution

Answer 1

1. False; Poisson Distribution  is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event.
2. True; One of the experimental conditions for Binomial Distribution is that the probability of success should be constant in each independent trial. So, for small binomially distributed populations it will not hold but for large binomially distributed populations this does not pose a problem.
3. True ; Let X~Trig(a,b) with peak at x=c. Comparing it with the question we get a=2, b=8 and c=7.Now, which is greater then 60%=0.6
4. True; It is so that the events are stochastically dependent, although random according to the defination of Hypergeometric Distribution.
5. True; according to the defination.
6. False; combination of n numbers is always smaller than the permutation of the same n numbers, taken the same number of times.
7. False; Events are said to be mutualy exclusive if the happening of any of them precludes the happening of all the others.
8. True; As each number 1 to 6 has equal probability of occuring in a fair die.
9. False; P(A/B) is a conditional probability of the event A< given that the event B has already occured.