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# MKT600 Test 1

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Department
Marketing
Course Code
MKT 600
Professor
Christopher Gore

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Bohdan Kaflyuk / Sec 021 Probability: is the numeric value representing the chance, like hood, or possibility a particular event will occur, such as the price of a stock increasing, a rainy day, a defective product, or the outcome five in a single toss of a die. There is 3 types of probability: A Priori, Empirical, Subjective. A priori probability : Probability of success is based on prior kProbability of occurrence: X. X= number of ways in which the event occurs / T= total number of possible outcomes. Ex: A die has 6 sides. Each face has a number 1 to 6. If you roll a die what's the probability? Solution: Each face is equally likely to occur. Since there is 6 faces, the probability of getting a face with 5 dots is 1/6. Empirical Probability: Probability based on observed data, not on prior knowledge of a process. Surveys are often used to generate empirical probability. Examples of this type of probability are the proportion of individuals in using Subjective Probability: Different from the other 2.ts , and 60% state that they have part time jobs , then the ratio is 6.0 for students having part time job. Probability distribution for a discrete random variable: is a mutually exclusive listing of all the possible numerical outcomes along with the probability of occurrence of each outcome. Random Variable: A variable whose value is determined by outcomes of a random experiment. SYMBOL used is usually X. Discrete random Variable: A random variable whose possible values are discrete, i.e. clearly separated individual values. Discrete Probability Distribution: A table or formula that shows the probability associated with each possible value of a discrete random variable. Let X = # cars sold on Sunµ= MeanSunday at a particular dealership shows that the following probability distribution exists: n ∑ XiP(Xi) Probability distributionµ= E(X)=: ------->Expected Value of a Discrete Variable. i=1 X P(x) µ= E(X) =∑ XP(X) -------------> Mean or Expected Value X−μ 2 ¿ 1 0.1 √ σ = ¿ ----------> Variance ∑ ¿ 2 X−μ¿ (¿ ¿P(X) ) σ 2 0.1 = ∑ ¿ ------> Standard Deviation ¿ √ ¿ 3 0.4 4 0.3 Total 1.0 The mean, µ, of a probability distribution is the Expected Value of its random variable. To calculate Expected Value: Multiply each possible outcomes, X, by its corresponding probability, P(X), and then sum these products.(of a discrete random variable) EX: (0)(0.01)+(1)(0.1)+(2)(0.2)+(3)(0.3)+(4)(0.15)........=2.8 Press: F6---> list:List1/XList: List/ Freq: List 2 ∑ ¿ i=1 √ ¿ 2 Xi−E X ¿ ( ) ¿ 2 2 ¿ Standard Deviation of a Discrete Random =ariable: = n List two:0.10, 0.10,0.2To get the answer press F1(Var 1) ∑ ¿ i=1 √ ¿ EX. Home Mortgages mean : 2.8 / x= 1.5684 2 Approved per Week P(X) XP(X) [X- E(X) P(Xi) i i i i i 2 0 0.10 (0)(0.10)=0(0-2.8) (0.10)= 0.784 σ 2 1 0.10 (1)(0.10)=0.(1- 2.8) (0.10)= 0.32=* √ σ = √ 2.46 = 1.57 2 0.20 (2)(0.20)=0............ 3 0.30 (3)(0.30)=0............. * The mean number of mortgages approved per week is 2.8, the Variance is 2.46,and the Standard Deviation is 1.57 5 0.10 (5)(0.10)=0............. 6 0.05 (6)(0.05)=0...... 2 1.00 μ = E(X)= 2.8 σ = 2.46 Mathematical Model: is a mathematical expression that represents a variable of interest. Binomial Distribution: is one of the most useful mathematical models. You use it when discrete random variable is the number of events of interest in a sample of N observations. F5F5---F1 OR F2 IF you want to find a probability even an exact amount of times THEN USE Bpd (Probability) X= # of successes / n= # of trials or sample space. / π= probability of success of each trial. / n!= n factorial(6!= 720) EX: toss coin 6 times, find probability of getting 2nCaRl/ n choose r / order doesn't matter. n= 6 / π= 0.5 / x = 2 CALC: F5 then F5 then F1 choose variable EX: Roll a die 10 times. Find the probability of getting EX: Survey of people in 30 and under 40 age bracket shows that 43 % of them investments in mutual funds. In a particular condominium are 18 x= # of 5's / n= 10 / π= 1/6....................CALC: x= 3 / numtriaadults in the age bracket. what is the probability that : - at most 2 of these people will have inv. in mutual funds? : CALC: (C.D) = 4.1007E.03--->= 0.0041007 Mean of Binomial Distribution: The mean of binomial distribution is equal to simple size ,n, multiply by the probability of an event of interest , π.: (C.D) e −A A x Poisson Distribution: P(X)= X! * P(X)= the probability of X events in an area of opportunity / A= expected number of events / e= Mathematical constant approximated by 2.71828/ X number of events( X = 0, 1 , 2 ...) μ CALC: F5--->F6--->F1--->F1 for (Ppd).........." symbol instead of "A"......................Ppd calculates p(X = #)............Pcd calculates P(X ≤ #) Normal distribution: EX: Suppose that the weights of adults are normally distributed when a mean of 170.0 lbs. and a standard deviation of 25.0 lbs. CALC: F5-->F1--->F2 A. what is the probability that a person weights from 150 to 190 lbs.? X= persons weight / = 170lbs / σ = 25.0 lbs.... CALC: lower =150/Upper= 1=25/ μ = 170...It will give you the answer. B. what is the probability that a person weights less than 140lbs? μ σ
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