1. STATISTICS “Probability Distribution” 8.0 Counting Principles & Probability Distribution

2. Random Variables –The outcomes of these experiments are considered random variables –A random variable is an outcome that takes on a numerical value as a result of experiment. The value of the random variable is often denoted by x. E.g. P[x=1] = 1/6 8.0 Probability Distribution

3. Random Variables –Random variables are categories into 2 type: a)Continuous random variables (The result of a measurement on a continuous number scale) b)Discrete random variables (The result of a counting outcomes rather than measuring them) 8.0 Probability Distribution

4. Continuous random variables 1.A random variable is continuous if it can assume any numerical within an interval as a result of measuring the outcome of an experiment. 2.E.g. The weight of Ali measured daily for the month →values CRV could be 80kg, 85kg, 81kg.. 8.0 Probability Distribution

5. Discrete random variables 1.A random variable is discrete if it is limited to assuming only specific integer values as a result of counting the outcome of an experiment. 2.E.g. The number of meal of Ali take in a month for him diet program →values DRV could be 2,1, 3… 8.0 Probability Distribution

6. Continuous vs Discrete CRV: 1) The amount of local rainfall, in inches this month 2) The length of time a customer required at a checkout lane in the grocery store 3) The speed of a vehicle travelling on the inter-state measured by a radar gun DRV: 1)The number of days during the month in which it rained 2)The number of customers standing in line waiting to check out at the grocery store 3)The number of cars that were found driving faster than the speed limit during the past hour 8.0 Probability Distribution

7. Probability Distribution 1.A probability distribution is a listing of all the possible outcomes of an experiment along with the relative frequency/probability of each outcome. 2.Probability distribution play a major role in the use of inferential statistics. 8.0 Probability Distribution

8. Discrete Probability Distribution 1.A listing of all the possible outcomes of an experiment for a discrete random variable along with the relative freq/probability of each outcome is called a discrete probability distribution 2.Mean of a DPD = μ = ∑ i =1 n X i * P[ Xi ] μ = the mean of the DPD X i = the value of random variable P[ X i ] = the probability of the ith outcome n = the no. of outcome in the distribution 8.0 Probability Distribution

9. Discrete Probability Distribution 3.The variance of DFD = σ² = ∑ 4.The std deviation of a DPD = σ = √ σ² μ = the mean of the DPD P[ X i ] = the probability of the ith outcome n = the no. of outcome in the distribution i =1 n (X i - mean)² * P[ X i ] X i = the value of random variable σ² = the variance of the DPD 8.0 Probability Distribution

10. TRY THIS!! A survey of 500 passengers was conducted to find how many luggages were brought along during their flight trip to their respective destinations. The following table summarizes the results: 8.0 Probability Distribution (x i )Freq 025 1185 2137 398 445 510 a) Develop a probability distribution for this data b) Calculate the mean, variance and standard deviation.

11. TRY THIS!! SPCA conduct a survey of 450 families to find how many cats were owned by each respondent. The following table summarizes the results: 8.0 Probability Distribution (x i )Freq 0137 1160 2112 331 410 a) Develop a probability distribution for this data b) Calculate the mean, variance and standard deviation.

12. Quiz 7