Consequently, we calculate Part 7 To find the variance of X , we use our alternate formula to calculate Finally, we see that the standard deviation of X is. Search for:. How to calculate a PDF when give a cumulative distribution function. The difference between discrete and continuous random variables. What a random variable is. In MATH , there are no difficult topics on probability. There are two types of random variables: discrete and continuous.
A discrete random variable is one which can take on only a countable number of distinct values like 0, 1, 2, 3, 4, 5…, 1 million, etc.
Some examples of discrete random variables include:. A continuous random variable is one which can take on an infinite number of possible values. Some examples of continuous random variables include:. For example, the height of a person could be There are an infinite amount of possible values for height. Rule of Thumb: If you can count the number of outcomes, then you are working with a discrete random variable e. But if you can measure the outcome, you are working with a continuous random variable e.
A probability density function pdf tells us the probability that a random variable takes on a certain value. For example, suppose we roll a dice one time. If we let x denote the number that the dice lands on, then the probability density function for the outcome can be described as follows:.
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James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you! Grateful I saw this at the right time for my CFA prep. Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures. Great support throughout the course by the team, did not feel neglected.
QBank is huge, videos are great. Would recommend to a friend. Professor Forjan is brilliant. In the following sections these categories will be briefly discussed and examples will be given.
Consider our coin toss again. We could have heads or tails as possible outcomes. If we defined a variable, x , as the number of heads in a single toss, then x could possibly be 1 or 0, nothing else. Such a function, x , would be an example of a discrete random variable. Such random variables can only take on discrete values. Other examples would be the possible results of a pregnancy test, or the number of students in a class room. Back to the coin toss, what if we wished to describe the distance between where our coin came to rest and where it first hit the ground.
That distance, x , would be a continuous random variable because it could take on a infinite number of values within the continuous range of real numbers. The coin could travel 1 cm, or 1. Other examples of continuous random variables would be the mass of stars in our galaxy, the pH of ocean waters, or the residence time of some analyte in a gas chromatograph. Mixed random variables have both discrete and continuous components.
Such random variables are infrequently encountered. For a possible example, though, you may be measuring a sample's weight and decide that any weight measured as a negative value will be given a value of 0. The question, of course, arises as to how to best mathematically describe and visually display random variables. Consider tossing a fair 6-sidded dice. We would have a 1 in 6 chance of getting any of the possible values of the random variable 1, 2, 3, 4, 5, or 6.
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