Random Variables and Probability Distributions

understanding random variables hi I'm doctor Nick and I'm going to help you learn what random variables are in what they do I will also explain discrete and continuous random variables in simple terms a random variable is the result of a chance event that you can measure or count for example in our probability videos we looked at the probability of giving a lunch with an apple and a banana cake this was the result of a chance event but it was not a random variable as it was not a number we will use the following example to learn about things that are random variables Luke has an ice cream stand and sells hand scoot homemade ice creams and cones Luke wishes to analyze the sales and make decisions about employing an assistant and expanding his business Luke has collected data from the last month and can tell you how many ice creams were bought in each transaction the table lists the number of ice creams board in the number of customers who bought that number of ice creams we can define X as being the number of ice creams a customer orders X is a random variable it is called random because it can take several different values and is the result of a chance happening we estimate the probability for each value of x by finding the relative frequencies from the historic or experimental data the distribution for X the number of ice creams one customer buys looks like this if the dot diagram it looks like this which could be rearranged to look like this we often like to show distributions as a graph we can use this distribution to answer questions Luke wants to know what is the probability that the next customer will buy exactly one ice cream we look on the table and tell him that the probability that x equals 1 equals 0.45 or 45% Luke then asks out of 200 customers how many would we expect to buy more than three ice creams we want to find the probability that X is greater than three so we add up all the probabilities that apply the probability that X is greater than three equals the probability that x equals four plus the probability that x equals five plus the probability that x equals six which equals point zero four plus point zero four plus point zero two which equals point one or 10% 0.1 times 200 equals 20 so we would expect 20 customers out of the next 200 to buy more than three ice creams this example of number of ice creams is an example of a discrete distribution as you can only get whole numbers of ice creams other things that can be modeled as discrete random variables our number of customers who arrive in the next hour number of customers who pay by cash number of days in a month in which the stall is closed due to rain number of cones that break while being filled the following cannot be modeled as discrete random variables because they cannot be counted the flavor topping a customer chooses the ethnicity of the customer the method the customer uses to pay some random variables are continuous which means that they can take any value within a range including fractions if we wish to model the weight of an ice cream it would take a range of values and grams so it would be modeled by a continuous random variable Luke is interested in how long he takes to serve a customer and he'll on to scoop an ice cream these would both be continuous random variables measured in minutes or seconds for each of the following decide whether they would be modeled as a discrete random variable a continuous random variable or not a random variable weight of a suitcase number of emergency calls in an hour marital status time taken to get to a fire length of a tulip stem color of a tulip flower number of bulbs that produce flowers you can see the answers at the end of the video here are the answers

Channel: Dr Nic's Maths and Stats

Views: 258,023

Keywords: Probability Distribution, Random Variable, discrete, continuous, help, tutorial, cochlear implant, understanding, AP statistics

Id: lHCpYeFvTs0

Length: 4min 38sec (278 seconds)

Published: Mon Jun 30 2014