Random variable

(ISOM2500)[2012](f)midterm1~=0zvopee^_78631.pdf downloaded by mhwongag from http://petergao.net/ustpastpaper/down.php?course=ISOM2500&id=0 at 2013-12-16 02:44:12. Academic use within HKUST only. Business Statistics, ISOM2500 (L3, L4 & L5) Practice Quiz I 1. The following bar chart describes the results of a survey concerning the relevance of study to present job by school. Focus on the School of Business and Management. What are the mode and the median respectively? (a) Relevant, Neutral (b) Relevant

An additive noise is characteristic of almost all communication systems. This additive noise typically arises from thermal noise generated by random motion of electrons in the conductors comprising the receiver. In a communication system the thermal noise having the greatest effect on system performance is generated at and before the first stage of amplification. This point in a communication system is where the desired signal takes the lowest power level and consequently the thermal noise

in a certain compound may be considered as a random variable, where X (0 < X < 1) has pdf fX (x) = 20x3 (1 − x), 0 < x < 1. Suppose that the selling price of the above compound depends on the alcohol contents. Specifically, if 1/3 < X < 2/3, the compound sells for c1 dollars/gallon otherwise it sells for c2 dollars/gallon. If the cost is c3 dollars/gallon, find the probability distribution of the net profit per gallon. 2. The pdf of a random variable X is given by fX (x) = 6x(1 − x), 0 < x < 1

probability that he makes fewer than 2 incorrect inspections is .736. A: Use Binomial table to discover , add 3 probabilities for 0,1,2 A continuous random variable may assume only integer values within a given interval. A: False A decision tree is a diagram consisting of circles decision nodes, square probability nodes and branches. A: False A table of random numbers must be normally distributed and efficiently generated A: False Simulation results will always equal analytical results if 30 trials

Simulation * Discrete Probability Distribution * Confidence Intervals Calculations for a set of variables Mean Median 3.2 3.5 4.5 5.0 3.7 4.0 3.7 3.0 3.1 3.5 3.6 3.5 3.1 3.0 3.6 3.0 3.8 4.0 2.6 2.0 4.3 4.0 3.5 3.5 3.3 3.5 4.1 4.5 4.2 5.0 2.9 2.5 3.5 4.0 3.7 3.5 3.5 3.0 3.3 4.0 Calculating Descriptive Statistics Descriptive Statistics: Mean, Median Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Mean 20 0 3.560 0.106

DESCRIPTIVE STATISTICS & PROBABILITY THEORY 1. Consider the following data: 1, 7, 3, 3, 6, 4 the mean and median for this data are a. 4 and 3 b. 4.8 and 3 c. 4.8 and 3 1/2 d. 4 and 3 1/2 e. 4 and 3 1/3 2. A distribution of 6 scores has a median of 21. If the highest score increases 3 points, the median will become __. a. 21 b. 21.5 c. 24 d. Cannot be determined without additional information

* Confidence Intervals Calculations for a set of variables Answer: Calculating Descriptive Statistics Answer: Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Mean 20 0 3.560 0.106 0.476 2.600 3.225 3.550 3.775 4.500 Median 20 0 3.600 0.169 0.754 2.000 3.000 3.500 4.000 5.000 Calculating Confidence Intervals for one Variable Answer: Variable N N* Mean SE Mean StDev Minimum Q1 Median

showing your calculation methods: • The marginal probability that any person selected at random from the population is a male. • The marginal probability that any person selected at random from the population is aged between 25 and 54. • The joint probability that any person selected at random from the population is a female and aged between 55 and 64. • The conditional probability that any person selected at random from the population is 25 or over given that the person is a male. QUESTION 2 Statistical

showing your calculation methods: • The marginal probability that any person selected at random from the population is a male. • The marginal probability that any person selected at random from the population is aged between 25 and 54. • The joint probability that any person selected at random from the population is a female and aged between 55 and 64. • The conditional probability that any person selected at random from the population is 25 or over given that the person is a male. QUESTION 2 Statistical

Queuing Theory: Queuing theory is described as the study of waiting lines (Render et al, 2015). Believe it or not it is a theory we use daily. Some instances you may encounter applying this theory, could be when deciding on which line to wait on when making a purchase or when initiating a phone call for service to be placed on hold. Sometimes when being placed on hold in queue the company, for example Comcast, may tell that you are the fifth person on hold or in queue; they may even give you