Question
T or F?
Please explain briefly for every answer
_1. The number of successes in "n" Bernoulli trials, X, has a binomial distribution. -2, A Random Variable is considered to be "continuous" if the number of possible values of X is finite. -3, when working with a discrete random variable, the probability of a random variable occurring in an interval does not depend on whether its endpoints are included. -4. GPSS stands for General Purpose Simulation Software -5. The normal distribution is a practical distribution to use to represent service time. 6. The fact that the probability that X lies in the interval [a,b] is given by Pasxsb)-Lfods implies that X is a Discrete Random -7. In the exponential distribution, the mean and the variance are always equal. B. The expected value of the random variable Xis denoted by E(X). 9. The two most important statistical properties of a Random Number Generator are Uniformity and Independence. 10. The exponential distribution is a good distribution to use to represent the number of random arrivals in a particular time period. -11. The Linear congruential random number generation method is known as the multiplicative congruential method if "a" is equal to zero. 12. When working with a continuous random variable, the probability of a random able occurring in an interval does not depend on whether its endpoints are vari included -13·The "Period" of a random number generator should be small. 14. The "seed" is the initial value in a random númber stream.
Explanation / Answer
1 ) TRUE
Reason : A Bernoulli trial has either a success or failure as outcome . Sum of n Bernoulli trials follows a binomial distribution by definition .
2 ) FALSE
Reason : A continuous random variable is a random variable where the data can take infinitely many values.
3 ) FALSE
4 ) TRUE
5 ) FALSE
Reason : Exponential distribution is used to represent service time .
6 ) FALSE
Reason : It implies that X is a continuous random variable .
7 ) FALSE
Reason : In exponential distribution mean and standard deviation are equal .
8 ) TRUE
9 ) TRUE
10 ) FALSE
11 ) TRUE
12 ) TRUE
13 ) FALSE
14 ) TRUE
