- #1
anaisabel
- 16
- 3
- Homework Statement
- Find integral of delta function in problem
- Relevant Equations
- equation 1 from solution
Can you elaborate a bit more, i am not understanding very well.vela said:I'd say it has to do with the fact that the range is maximum when ##\theta = \pi/4##.
I don't see how it couldn't be. If the crocodile were infinitely long and lying on the +x axis, for instance, the probability of hitting it would be 1.anaisabel said:The length of the crocodile isn't really relevant.
What have you tried to do in evaluating the integral?anaisabel said:I have forgotten a bit of my calculus, so I know the distance is the same, but if i don't know why it would complicate?.
In when comes to length of the cocrodile, I haven't gotten that far because I can't solve the integral. I have tried to solve it, and I understand now why you have to separate in two intervals, from 0 to pi/4 and pi/4 to pi/2, because when you perform tha change of variable and change the limits it would go from 0 to 0 if you didnt break into intervals. I understood that, but what I don't understand after. After I separate into intervals and perform the change of variable y like it is in my attempt, I don't know how to evaluate the integral, using the equation 1. The density is 2/pi, so is a constant, so what is the meaning of what is inside of delta?vela said:I don't see how it couldn't be. If the crocodile were infinitely long and lying on the +x axis, for instance, the probability of hitting it would be 1.What have you tried to do in evaluating the integral?
A delta function, denoted as δ(x), is a mathematical function that is commonly used in physics and engineering to represent an impulse or spike of a certain magnitude at a specific point. In terms of calculating density of probability, the delta function can be used to represent the probability of an event occurring at a specific value of a continuous random variable.
The delta function is directly related to the concept of probability density, as it is used to represent the probability density function (PDF) of a continuous random variable. The area under the delta function curve represents the probability of an event occurring at a specific value, and the integral of the delta function over a range of values gives the probability of the event occurring within that range.
Yes, the delta function can be used to calculate the probability of a continuous random variable taking on a specific value. This is because the delta function has a value of zero everywhere except at the specific value, where it has a value of infinity. When integrated over a small range around the specific value, the delta function gives a finite probability for the event occurring at that value.
One limitation of using the delta function to calculate density of probability is that it can only be used for continuous random variables. It cannot be used for discrete random variables, as they have a finite number of possible outcomes. Additionally, the delta function can only be used for events that have a probability of occurring at a single point, and cannot be used for events that have a probability of occurring over a range of values.
The delta function is a special case of the Dirac delta function, which is a more general mathematical concept used in various fields of science and engineering. The Dirac delta function can be used to represent other probability distributions, such as the Gaussian distribution, by convolving the delta function with the desired distribution. This allows for the use of the delta function in a wider range of applications beyond just calculating density of probability.