What is Probability distribution: Definition and 201 Discussions

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). Examples of random phenomena include the weather condition in a future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc.

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  1. Avatrin

    What is this well known probability distribution?

    Homework Statement I have a probability density function: f_{X}(x) = θk^{θ}x^{-θ-1} when x > k and 0 everywhere else And: Y = θlog(X/k) Find the probability density function for Y. What well known density function is this? Homework Equations I don't really know where to start...The Attempt at...
  2. S

    Conditional Probability Distribution

    Homework Statement The Attempt at a Solution I have that the joint probability mass function would be \Pi_{i=1}^{k} \frac{\lambda_{i}^{n_{i}}}{n_{i}!} e^{-\lambda_{i}} How would I go about applying the conditional to get the conditional distribution?
  3. K

    Normal and uniform probability distribution.

    Am I right? Thank you!Problem: A cereal brand of cereal claims that the mean number of raisins in each box is 80 with a standard deviation of 6. If the raisins are normally distributed, what are the chances that an arbitrary box has 1) fewer than 70 raisins and 2) more than 90 raisins. What...
  4. B

    Simple probability distribution function on gnuplot

    Hi, I am trying to plot a graph I have made using excel on gnuplot. I have converted the excel book to a csv file and the data I have looks like this 0,0.166341305 1,0.000000159 2,0.000000159 3,0.000000159 4,0.000000159 5,0.000000159 ... and so on for 2048 different points. The data...
  5. B

    MHB Probability distribution of a RV is a function of another RV

    Dear friends, I have a Random Variable I. Sample space of I is from 1,2,3... inf(countably infinite). It's probability distribution P(I=i) is a function of another set of Random Variables Xi's, which are uniformly distributed in [0,1]. These Random variable are iid. I have to find out the mean...
  6. B

    MHB Probability Distribution of Geometric Random Variables

    Dear friends, I have divided the time into slots of fixed size. And i toss a coin of probability of heads 1/2 in the first slot. In the next slot, i toss a coin of probability of head 1/4, and in the i^th slot i toss a coin of prob of head 1/2^i. I do this until i get a head. What is the...
  7. M

    Multivariable Probability Distribution

    f(x,y) = ke^(-x-y), 0<x<∞ , 0<y<∞ , and x<y Find k to make this a PDF. So I set up: ∫(from 0 to ∞)∫(from 0 to ∞) [ke^(-x-y)]dxdy. Is this integral right? I also need to find the marginals of X and Y but my k has to be right first.
  8. N

    Adiabatic approximation for joint probability distribution

    Hi group, I'm a theoretical ecologist with fairly adequate training in applied math (ODE, linear algebra, applied probability, some PDEs). In my current work, I've encountered the use of adiabatic approximation to a joint probability distribution of two ever-fluctuating spatial variables. A...
  9. A

    Joint probability distribution of two images

    I'm posting this here, as i feel it's more probability-related than image processing. I'm reading this lecture pdf. At end of page 1 , beginning of page 2 it says: Is this a bit vague, or am i missing something? Since we are calculating frequency of the value a in the pixels of image A, when...
  10. B

    Radial probability distribution (rpd)

    Radial Probability Density = R(r) : Square of the Radial Wavefunction The required volume is determined by the volume of the SPHERICAL SHELL enclosed between a sphere of radius (r+dr) and a sphere of radius r rpd = radial probability density × volume of the spherical shell = R2 × 4πr2 drhow...
  11. M

    Probability distribution pin code guessing

    Homework Statement What is the distribution of stochastic variable X = "the number of attempts needed to find the correct last digit of a pin code" Homework Equations The Attempt at a Solution I thought it was like this: P(X=1) = 1/10 P(X=2) = 9/10*1/9 P(X=3) = 9/10*8/9*1/7...
  12. S

    Russian Roulette probability distribution

    Hi. This isn't exactly like the previous thread and not a homework problem. I'd just like to check the validity of my solution. It concerns the relation between a discrete and continuous probability distribution. The problem: A player inserts a bullet into a 6-chamber revolver. He then spins...
  13. L

    What is the name and application of this probability distribution

    Hi. In my homework I've encountered a discrete probability distribution of this form: f(k,\lambda)=N \frac{\lambda^k}{k!} k is the variable, and \lambda is a parameter. I'm curious what is this distribution - what's its name and where can it be applied. I will be grateful for, for...
  14. C

    What is the process for finding the constant A in a probability distribution?

    Homework Statement Probability distribution for finding an object that can move anywhere along an x-axis is given by P(x) = A x^2 exp(-x^2/a^2) The Attempt at a Solution I need to find A so it correctly represents a probability distribution. Am I right in thinking I need to...
  15. L

    What is the Expected Number of Retransmissions?

    Homework Statement Assume that the probability of error-free transmission of a message over a communication channel is p=0.9. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Such a channel is often called...
  16. P

    Calculating probability distribution for rolling 4 dice plus reroll lowest die

    Hi, I am trying to figure out what the probability distribution is for the following: 1. Roll 4 dice. 2. Take the lowest die and re-roll it. 3. Take the sum of the three highest dice. The result will be between 3 and 18. I know how to figure out the probability distribution for...
  17. M

    Continuous Probability Distribution Question

    Homework Statement Homework Equations The Attempt at a Solution I can show the second one, i.e. 1/3 [sqrt(y) +1] and need help in showing the first one. Can anyone guide me?
  18. O

    How Can I Assign Probabilities Based on Latency Proximity?

    Hello All, I calculated an average latency value let say 3 units then after observing the network I found that different nodes have the fallowing differnt latency i.e. 4, 5, 6, 7, 10 units. now I need to assign probability to each latency considering that the value which is more closer to...
  19. M

    Probability distribution in a quantum well

    Homework Statement Consider a mixed state comprising equal components of the first two energy levels in an infinite QW of width L. These have (normalised) wavefunctions ψ1 and ψ2. The wavefunction for the mixed state will be ψ(x,t)=(1/√2)ψ1e^(iw1t)+(1/√2)ψ2e^(iω2t) a) Calculate the...
  20. S

    Probability Distribution and Confidence Interval

    Homework Statement Let X1, X2,...Xn be a random sample from the distribution with probability density function fX (x;θ) = (θ+1)(1-x)θ, 0<x<1 θ>-1 a) What is the probability distribution of Y= -\sum ln(1-Xi from i=1 -> n b) Suggest a (1-α)100% confidence interval for θ based on Y=...
  21. I

    Mode of a probability distribution

    Homework Statement I have a luminosity prob distribution that i want to plot and find the expectation value and mode for. Homework Equations p(L)dL = A \frac{L}{i}^aexp(-\frac{L}{i}) \frac{dL}{i} A=const a= -0.7 i= 1.4e10 solar luminosity units lower limit = 1e9 solar luminosity...
  22. B

    Probability distribution of classical momentum

    Suppose I solve the Schrodinger wave equation described in terms of position (as opposed to momentum based description), it gives me the wave function from which I can determine the probability distribution function (pdf) for position with a parameter as time. I view it as the following, the...
  23. A

    Probability Distribution Problem

    Homework Statement Log-ons to a certain computer website occur randomly at a uniform average rate of 2.4 per minute. State the distribution of the number N of log-ons that occur during a period of t minutes. Obtain the probablity that at least one log on occurs during a period of [I]t...
  24. J

    Radial Probability Distribution Curve for Hydrogen Atom

    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...
  25. K

    Help with probability distribution for description of particle sizes

    I study nanoparticles. Basically, they are prepared by being "etched away" from larger chunks of material. I need to describe their sizes, i.e. fit the histogram of measured sizes, with a probability distribution. The measured distribution is clearly asymmetrical with a tail toward larger sizes...
  26. C

    Cellular network Probability distribution function of frequency

    Hi, I am trying to model a PDF of frequency for the WCDMA handset. I have found some info on ways of graphing a PDF of transmit power but nothing on frequency. I am hoping there is a way to model this, but think it might be something that requires field tests with multiple phones. Any...
  27. T

    Help with probability distribution function question

    Homework Statement Let X and Y be two independent random variables with the same probability density funtion over: f(x) = {1/a if x € [0,a] {0 if x=0 Find the density distribution of a) X + Y and b) X*Y Homework Equations The Attempt at a Solution Ok, my...
  28. U

    Combined probability distribution

    Homework Statement Let's have a box in shape of a square(viewed from the top) from the corner of which a smaller square was cut out.The side of a bigger square is 2a, side of the smaller square is a long. We've got evenly distributed corn seeds all over the box,randomly selected seed is...
  29. M

    Poisson probability distribution

    Homework Statement Homework Statement A particle detector is set up to detect type A particles. These are detected as a poisson process with parameter lamda = 0.5 per day. (i) What is the probability that 3 or more will be detected in anyone day? (ii) What is the distribution of...
  30. S

    Exploring Stochastic DiffyQ: How to Get a Probability Distribution for V(t)?

    Hello all, I have run into this problem, and being that I know nothing about stochastic DiffyQ I am trying to toy around with it. Basically, the following is a boiled down version of my problem: I have a probability density function that is given: p(t) and let's say we pick 1 value from...
  31. D

    Probability distribution, find constant

    Homework Statement x = 0, P(x) = 0.4 x = 1, P(x) = 0.1 x = 2, P(x) = 0.1 x = 3, P(x) = 0.1 x = 4, P(x) = 0.3 If P(x)=k(5-x) for x = 0,1,2,3,4, find value of constant k The Attempt at a Solution 0.4 = k(5-0) 0.1 = k(5-1) 0.1 = k(5-2) 0.1 = k(5-3) 0.3 = k(5-4)...
  32. J

    Probability distribution for hard sphere elastic collisons

    I'm researching neutron moderators and I want to model how many collisions are required for fast neutrons to be moderated to thermal temperatures and the distribution of energy absorbed by the moderator during the process. I have quickly worked out the %age velocity reduction for the simple head...
  33. E

    Needle probability distribution problem

    Homework Statement part a(complete) The needle on a broken car speedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 and \pi. part b(attempting) We consider the same...
  34. P

    Probability Distribution Function

    Homework Statement Given the probability distribution function: See attachment. Determine the: 1. Probability density function. 2. The mean. 3. The median. Homework Equations Hello, I am really struggling with this subject area, this is an example I have found, would...
  35. Y

    Probability distribution confusion

    Hi, I am trying to write a Monte Carlo type simulation. I have a function for the probability (p) of a photon having an angle (a) between \theta and \pi/4 defined by: p = \int_{a= \theta}^{a=\pi/2} \cos(2a),\qquad da ...where \theta will normally have a value between -\pi/4 and \pi/4. One...
  36. T

    For the following probability distribution

    Question : For the following probability distribution X | -1 | 0 | 1 | Y | 0 | 1/15 |2/15|1/15| 1 | 3/15 |2/15|1/15| 2 | 2/15 |1/15|1/15| Find i )The conditional distribution of X given Y=2 Solution f(x|2) = f(x,2) / h(2) How do i go about this without knowing f(x,2)
  37. T

    Probability Distribution function change of variables.

    Homework Statement I have been given the distribution function F_X of the random variable X and I am asked to find the distribution function F_Y of Y, another random variable which is defined from X in the following way. Y={\stackrel{X^{2} if X<2;}{4 if 2\leq X < 3;}\stackrel{4(4-X) if...
  38. A

    Probability distribution function question

    Homework Statement A PC generates "random" numbers from [0,1], programmed such that the distribution function F(x) of a continuous random variable X, which is satisfies the formula: F(x) = 0 , x<0 x , 0<=x<0.25 0.25 , 0.25<=x<0.5 x2, 0.5<=x<1 1 , 1<=x THe problem then asks the values of...
  39. M

    Finding the Probability distribution function given Moment Generating Function

    Hi everyone, So I am taking a statistics course and finding this concept kinda challenging. wondering if someone can help me with the following problem! Suppose X is a discrete random variable with moment generating function M(t) = 2/10 + 1/10e^t + 2/10e^(2t) + 3/10e^(3t) + 2/10e^(4t)...
  40. J

    Marginal probability distribution

    I have a question I need to answer. f\left(x,y\right)= 6x^2y such that 0<x<y and x+y<2 where f\left(x,y\right) is a probability density function for two random variables: X,\;Y I need to find marginal density distribution for the random variables X and Y It appears to be a straight forward...
  41. A

    Need help with expected value of probability distribution

    Homework Statement I'm trying to find the expected value of a probability distribution. Homework Equations \int_{-\infty}^\infty xP(x,t) = \int_{-\infty}^\infty x \frac{1}{\sqrt{4\pi Dt}}e^{-\frac{(x-dt)^2}{4Dt}}dx The Attempt at a Solution I expect the value to be something like...
  42. X

    Solving a Relativistic Ideal Gas Momentum Probability Distribution

    Homework Statement For a relativistic ideal gas, the momentum probability distribution is given by where http://latex.codecogs.com/gif.latex?\epsilon_p=\sqrt[]{m^2c^4+c^2p^2}. Determine A Homework Equations The Attempt at a Solution I know that...
  43. T

    Continuous probability distribution

    Homework Statement A continuous random variable ,X represents the period, of a telephone call in the office. The cdf of x is given by F(x)= x^2/8 for 0<=x<=2 =1-4/x^3 for x>2 Find pdf , mean and variance. Homework Equations The Attempt at a Solution pdf: f(x) = 1/4...
  44. J

    Anyone recognize this single parameter discrete probability distribution?

    I have a single parameter discrete probability distribution defined over the domain of non-negative integers with pmf in k of: Pr(k;L) = \frac{L^{k}}{k! * k! * I_{0}(2*\sqrt{L})} Where I_{0}() is the modified Bessel function of the first kind with order 0. I do know that E(k^{2}) = L...
  45. I

    Interpreting the probability distribution of the potential step

    Say you have a potential step problem where the potential steps up from V=0 to V=V_0 at x=0. If the incident particle has energy E <V_0, you get a non-normalisable solution for the wavefunction. How can you interpret |\psi|^2 for this non-normalisable solution? Is it still the probability...
  46. L

    Probability: joint probability distribution problem?

    Homework Statement John and George are set to meet each other at 12 o'clock. John's time of arrival, J, is distributed uniformly between 12:00 and 12:15. John will wait for George for 15 minutes. If he doesn't show up, he leaves. George's time of arrival, G, is also uniformly distributed...
  47. B

    What kind of probability distribution would you use to model network queues

    As an example, say 10 computers are connected to the network through 1 cable, (and so only 1 can be connected at anyone time) and each computer needs to be on the network for 12 minutes an hour on average, then what kind of pmf would you use to model the number of computers that simultaneously...
  48. S

    Confusing use of notation in expressing probability distribution

    Hi, I'm trying to follow a text about Bayesian statistics, and the author is using the following notation to describe a random variable which has normal distribution: p(x | µ, σ2) = (Gaussian density function here) In a Bayesian text, this notation is confusing, since it makes me think...
  49. S

    Probability Question About The Poisson Probability Distribution

    Probability Question About "The Poisson Probability Distribution" Homework Statement - Assume that 1 in 200 people carry the defective gene that causes inherited colon cancer. A sample of 1000 individuals is taken. Use the Poisson approximation to calculate the appoximate standard deviation...
  50. E

    Poisson Probability Distribution

    Homework Statement Suppose that .10% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 10,000 computers. a.)What are the expected value and standard deviation of the number of computers in the sample that have the defect? b.) What...
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