What is Probability function: Definition and 36 Discussions

A probability distribution function is some function that may be used to define a particular probability distribution. Depending upon which text is consulted, the term may refer to:

a cumulative distribution function
a probability mass function
a probability density functionThe similar term probability function may mean any of the above and, in addition,

a probability measure function, as in a probability space, where the domain of the function is the set of events.

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1. A Calculating Probability of N Points on a Line Being Within Given Distance

Probability of any random n points on a line being within a given distance Hi, I am a software engineer trying to solve the following problem analytically given a line segment in cm and n random points on it what is the probability that the distance between any 2 consecutive points on the...
2. What is the ideal number of guesses to maximize your marks in MCQs?

To approach this, I first assumed the case when the students attempts all the remaining questions. Probability that they gain 4 marks for a guess = ##\frac 1 4## Probability that they lose 1 for a guess = ##\frac 3 4## Now let us say the number of correct guesses = ##r## Now we should have at...
3. M

I Probability function for discrete functions

My textbook says that if ##X: \Omega \to \mathbb{R}## is discrete stochast (I.e., there are only countably many values that get reached), then it suffices to know the probability function ##p(x) = \mathbb{P}\{X =x\}## in order to know the distribution function ##\mathbb{P}_X: \mathcal{R} \to...
4. I Probability density of an exponential probability function

I have a model where the probability is spherically symmetric and follows an exponential law. Now I need the probability density function of this model. The problem is the singularity at the origin. How can I handle this? P(r) = ∫p(r) dr = exp(-μr) p(r) = dP(r)/(4πr²dr) One way I tried to...
5. I

Does the Radial Probability Function Indicate Angular Nodes?

Homework Statement I have a quick question, Does radial probability function of finding electron (4πr2R2) show only radial nodes, or does it show angular nodes too. (I am like 90% sure that it shows radial nodes only) Homework Equations N/A The Attempt at a Solution N/A
6. Probability function being imaginary?

Suppose ψ1 and ψ2 are two eigenfunctions of a particle and ε1 and ε2 are the corresponding eigenvalues. If the state is in the superposition Ψ = αψ1 + βψ2 at time t=0, it evolves in time by the equation Ψ = αψ1ei ħ/ε1 t + βψ2ei ħ/ε2 t. I am trying to understand the probability amplitude Ψ*Ψ.If...
7. Probability of finding a particle in a 1D box

Homework Statement If a one-dimensional box is 1 nm long, what is the probability of finding the particle between the following limits? (a) x = 0 nm and x = 0.05 nm (b) x = 0.55 nm and x = 0.65 nm Homework Equations ψ = (2/L)½ sin(πx/L) The Attempt at a Solution (I do chemistry and I'm really...
8. -- cumulative distribution function, probability density

Homework Statement For the next probability function: f(x)=x/4 for 0<x<2 Homework Equations a) Get the probability function b) Get the cumulative distribution function The Attempt at a Solution I don´t know if the problem is well written, and for that I'm lost with the first question...
9. Is wave function a probability function of time?

Wave function ψ(x,t) is a fuction of probability which depends on time example Ψ(x,t)=1/(c-v)t Let's suppose its a function of probability It depends on time and it affects space. Is this is a definition of wave function ? (I know wave function squuared gives probability...
10. MHB Probability function and random variables

Given a Bernoulli r.v., W, which is derived from r.v. T(Poisson) (a)if T=0 then W=1 and b) if T>0 then W=0). One has to show that the sample mean (the proportion of 0s in the sample), is an unbiased estimate of φ=e^λ. Also, how does one find the variance of the sample mean and show that this...
11. MHB Probability function (p.f) of a random variable

If one has a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any suggestions about how to proceed forward?
12. Solve f(x) = ce^-x, Find E(x) and Probability Generating Function

Here is the question, f(x) = ce^-x , x = 1, 2, 3... Find the value of c. Find the moment generating function of X. Use the result obtained, find E(x). Find the probability generating function of X. Verify that E(x) obtained using probability generating function is same as the first E(x)...
13. MHB Probability Function of Z: 1/4 & 1/2 Explained

Consider flipping two fair coins. Let X = 1 if the first coin is heads, and X = 0 if the first coin is tails. Let Y = 1 if the second coin is heads, and Y = 5 if the second coin is tails. Let Z = XY. What is the probability function of Z? how did you get 1/4 and 1/2 ?? and why? confused!
14. Kinda help Probability function - E(2^X)?

Kinda urgent help! Probability function - E(2^X)?? Question A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t) Find the pmf of X My solution x f(x) 1 0.3 2 0.4 3 0.6 5 0.1 The next question asks Calculate E(2^X) Which I am totally...
15. Standard Deviation in terms of Probability Function

Homework Statement I've still yet to learn Latex since I'm pretty good with words equation editor, so here's the question typed out in words. Homework Equations I really don't know what to do here. The Attempt at a Solution
16. How Does the Binomial Coefficient Calculate Combinations?

Homework Statement Homework Equations The Attempt at a Solution do you see where it says 5 over 2 = 10 and 5 over 3 = 10. How? I don't get what they're doing.
17. Convergence of Probability Function for E(|X|)

Hi guys, I have a question. E(|X|) < infinity iff E|X|I(|X| > n) -> 0 as n goes to infinity, where I is the indicator function.=> this direction is easy and I have it solved. I wonder if anyone has any idea of how to deal with <=. Thanks.
18. Probability function with specification for different ranges ?

The function fx(x) is defined differently for the range 0 to 1 as for values greater than one to 2. Past x = 2, the function is zero. When you are asked to find the expected value or variable how are the multiple ranges is all treated ? Do you need to add both functions together and...
19. Infinite well problem, not normal probability function(?)

Homework Statement A particle with mass m is trapped inside the infinite potential well: 0<x<L : U(x) = 0 otherwise: U(x) = ∞ ψ(x,t=0) = Ksin(3∏x/L)cos(∏x/L) What energies can be measured from this system, what are the probabilities for these energies ? Homework Equations Schrödinger...
20. Probability function with specification for different range ?

I understand a probability function can be defined according to range ? So for example, 0>x f(x) = 0 for 0>x>100 f(x) = 1/100 to work out probability it is integration of that function. So how does it work if for some other range there is a DIFFERENT functions ? Is it that...

22. How do you use a probability function in a simulation

Homework Statement i need to model the wind in a computer program. it is for a wind turbine model and I can use wind data that I have found on the internet, however I would prefer to see if I could model the wind using the weibull distribution and add on the kaimal spectrum if possible. The...
23. Probability function of two random variables, another non-convergent integral

Homework Statement The joint probability density function of the random variable (X, Y) is given by: f(x,y) = \frac{2x}{y^2} \text{where} \; 0 \leq x\leq 1 \; \text{and} \; y\geq 1 and 0 elsewhere. Find the probability density function of the folowing random variable: U=X+Y...
24. Rutherford scattering differential probability function

Homework Statement Spray of alpha particles hit a gold membrane whose density is \rho and thickness d, with a kinetic energy of E_k. The spray's intensity is I. Alpha particles are measured from an area of A which is set R away from the membrane. If \theta is the angle between the spray...
25. Plotting a Radial Probability Function

I'm trying to plot the radial probability function for a hydrogen atom. I have the function itself (Psi2*4*pi*r2) my problem is that when I plot the function with angstroms on the x-axis, the y-values are larger than they should be (they look about right if I divide them by the bohr radius in...
26. Probability Function Homework: Solving Parts (d), (e) & (f)

Homework Statement Hi I am trying to solve the d, e and f parts of this problem The discrete random variable X has probability function where k is a positive constant. P(X = x) ={k(2 – x), x = 0, 1, 2, k(x – 2), x = 3, 0, otherwise, (a) Show that k = 0.25...
27. Probability function of a discrete random variable

Homework Statement 10 face cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over one at a time, moving from left to right. Let X be the random variable for the number of cards turned before the ace is turned over. What is the probability function...
28. Finding the expected value of a probability function

1. Suppose X is a random variable with probability function f(x) = 0.49x(0.3)^ (x-1). Find E(x). 2. E(X) = sum of all x of x*f(x) 3. so I know that E(X) = sum of all x of x*f(x) so E(x)= 0.49* sum of all x of x^2(0.3)^(x-1) But I'm not sure how do i evaluate the sum? Can...
29. [PROBABILITY] Joint probability function for two DISCRETE variables

Homework Statement X1 and X2 represent the values of two honest dice throws (independent of each other). Find the joint probability function of U and V when: a) U = min{X1,X2}, V = X1 + X2 The Attempt at a Solution This is what I thought: P(U = u,V = v) = P(\min \left\{...
30. Probability function of a discrete random variable problem

Homework Statement Ten cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over oen at a time, moving from left to right. Let X be the random variable for the number of cards turned before the ace is turned over. What is the probability function for...
31. Integral of the Square of density probability function

Hi, I'm looking for the value of the integral of the square of a density probability function on a bounded interval. Tks
32. The probability function of electrons occupying the donor state

In Semiconductor physics and devices: basic principles [By Donald A. Neamen], chapter 4, section 4.4, it says: =================================================================== One postulate used in the derivation of the Fermi-Dirac probability function was the Pauli exclusion principle...
33. Calculating Marginal Probability Mass Functions for Discrete Random Variables

I have this question which I cannot seem to solve: The joint probability mass function p(x, y) of two discrete random variables X and Y is given by. p(x,y) = ([5^x][7^y][e^-5])/x!(y-x)! x and y are non-negative integers and x <= y (i) Find the marginal probability mass functions of X and Y.
34. Casio fx-991ES probability function

Hi Guys I need some one to help my to solve probability problems by Casio fx-991ES
35. Recursive probability function

I'm not sure if I should be posting here or in General, but here goes. I have a probability problem and I'm trying to get a closed form, or something resembling it, for a tricky recursive formulation. This problem is the 'simple' base case for a much more complicated problem, but I think I can...
36. What is the Distribution of Tossing a Die Until a 6 Appears?

I got really really confused by this supposedly easy discrete probability problem: The problem asks: a)toss a die until a "6" appears. Find the probability distribution of X where X is the number of tosses neded to obtain the first six. b) Prove that the summation of P(x) from x = 1 to n...