Section 3.6: Generation of Discrete Random Variables3.78. Octave provides function calls to evaluate the pmf of important discrete random vari-ables. For example, the function Poisson_pdf(x, lambda) computes the pmf at x for thePoisson random variable.(a) Plot the Poisson pmf for λ = 0.5, 5, 50, as well as P[X ≤ k] and P[X > k].

Octave code to plot the Poisson pmf for λ = 0.5, 5, and 50, as well as P[X ≤ k] and P[X > k]: %…

Answered: provides importan rando ables. For…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

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EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 0
Three statistically independent random variables X₁, X₂ and X₂ have mean values X₁ =3, X₂ = 6 and X₂ = -2. Find the mean values of the following functions: 1 2 (a) (b) g(X₁, X₂, X3)= X₁ +3X₂ + 4X3 29 g(X₁, X₂, X3) = X₁X₂X₂ 29
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Let X1 and X2be independent exponential random variables: fX1(x1) = e−x1 and fX2(x2) = e−x2 1
5 Calculate XkYk for the n = 5 data points (×₁,Y₁ ) = (2,4), (×2,Y₂) = (3,5), (×3,Y3) = (4,8), (×4,Y4) = (5,10), and k=1 (X5,5) = (6,14). 5 Σ xxYk = [ k=1 (Simplify your answer.)
Data collected over a number of years show that whena broker called a random sample of eight of her clients,she got a busy signal 6.5, 10.6, 8.1, 4.1, 9.3, 11.5, 7.3, and5.7 percent of the time. Assuming that these figures canbe looked upon as a random sample from a continuous uniform population, use the estimators obtained in Exer-cise 57 to estimate the parameters α and β.
1)Begin with the formula of the Durbin Watson DW statistic and the coefficient of first order autocorrelation p presented below in red and green colors. Derive another formula for the DW statistic, as a function of p, explain the mathematical steps in this derivation • DW = Σ-2(et-et-1)² Σ ef ΣΤ_20p@t-1/ Coefficient of serial Correlation p = Et et
Part II: Sections 2.1 2.7 7. Suppose that X is a discrete random variable with pmf f(x) =D c.14-피 . 뉴- 21 for r=-3, 3, 6, where c is a constant. (a) Find c. Compute E ( ~LX +) (b) 3.
X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is below
Consider a random variable V modeling the version of the software that people have installed on their computers, where the possible versions are {1, 2, 3, 4}. People are equally likely to have versions 1 and 2 and also equally likely to have versions 3 and 4. People are also x times more likely to have version 3 than version 2. (a) What is the (probability mass function) PMF of V as a function of x (b) What is the expected version of the software. Hint: the expected value of V as a function of x (c) What is the minimum value of x to ensure that the mean version is at least version 3?
Suppose the number of photons emitted by an atom during a one-minute time window can be modeled as a Poisson random variable with parameter λ = 2. Now, suppose you watch the atomfor two minutes, and the number of emitted photons in each minute is an independent Poisson process. Calculate the probability that you see exactly one photon during the two minutes. (Hint: this is the probability that you see no photons in the first minute and one photon in the second minute, plus the probability that you see one photon in the first minute and no photons in the second minute.) Similarly calculate the probability that you see exactly two photons during the two minutes.Compare these probabilities to the probabilities that a Poisson random variable with parameter λ= 4 takes the value one, or two. Are they the same?

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provides importan rando ables. For example, the function Poisson_pdf(x, lambda) computes the pmf at x Poisson random variable. to (a) Plot the Poisson pmf for λ = 0.5, 5, 50, as well as P[X ≤ k] and P[X > k]. A