We will now continue and derive some additional properties of probability laws which are, again, consequences of the axioms that we have introduced. The first property is the following. If we have two sets and one set is smaller than the other– so we have a picture as follows. We have our sample space. And …
Probability – L01.6 More Properties of Probabilities Read More »
The probability axioms are the basic rules of probability theory. And they are surprisingly few. But they imply many interesting properties that we will now explore. First we will see that what you might think of as missing axioms are actually implied by the axioms already in place. For example, we have an axiom that …
Probability – L01.5 Simple Properties of Probabilities Read More »
We have so far discussed the first step involved in the construction of a probabilistic model. Namely, the construction of a sample space, which is a description of the possible outcomes of a probabilistic experiment. We now come to the second and much more interesting part. We need to specify which outcomes are more likely …
Let us now look at some examples of sample spaces. Sample spaces are sets. And a set can be discrete, finite, infinite, continuous, and so on. Let us start with a simpler case in which we have a sample space that is discrete and finite. The particular experiment we will be looking at is the …
Putting together a probabilistic model- that is, a model of a random phenomenon or a random experiment- involves two steps. First step, we describe the possible outcomes of the phenomenon or experiment of interest. Second step, we describe our beliefs about the likelihood of the different possible outcomes by specifying a probability law. Here, we …
L 01.1 – Overview
Welcome to the first lecture of this class. You may be used to having a first lecture devoted to general comments and motivating examples. This one will be different. We will dive into the heart of the subject right away. In fact, today we will accomplish a lot. By the end of this lecture, you …
Rapid transfer of energy to a mechanical system which results in significant increase in stress, velocity, acceleration or displacement within the system is called a shock. Ek system ki natural frequency 200 Hz hai, matlab system apne aap 200 cycles per second mein vibrate karta hai jab usse disturb kiya jaye. Shock ke baare mein …
Sine vibration ke specifications ko define karte waqt velocity ke form mein na dene ke kaaran technical aur practical aspects se jude hain. Main reasons yeh hain: Example:Agar ek sine vibration test mein 10g acceleration at 200 Hz diya jaye, toh velocity calculate kar sakte hain: Conclusion:Velocity ke form mein specs na dene ka reason …
Why velocity is not given in the specification of vibration testing? Read More »