Write a function my_random that samples a random number from the following discrete probability distribution on the set {8, 9, 13, 15, 17, 18}:P({8}) = ²/9P({9}) = ²/18P({13}) = 1/P({15}) =P({17}) = ²/16 NOP({18})= =

To create a function my_random that samples a random number from the given discrete probability…

Answered: Write a function my_random that samples…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 5P

See similar textbooks

Similar questions

Using the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.
4. Write a Julia function called resistance that returns the resistance distance r given the Cholesky factor U of L+ ee" and nodes i and j. rij = resistance (U, i, j)
Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B
This assignment is to a analyze a random experiment. Assume that you have to toss a fair coin (50% probability for each head and tail) N times, where N→ 00, When head comes up, you will be rewarded (gain) RM1, while if tail comes up, you will be penalized (loss) RM1. Write a function function sum_return coin_toss (N) that returns a row vector sum_return of length N+1. Each column i represents gained sum from i-1 number of coin tosses, i.e. sum_return (1) =0. To solve this problem, you will need both a for statement and the rand function. Try out several (minimum of 2) tries a value of N of 1000, 10000, 100000, 1000000 and plot the results. The x-axis must show the values from 0 to N. The y-axis should be limited to the maximum gain and minimum loss during each experiment. Note that as N is large, plotting N points will take a long time. Find a way on how this can be made faster.
The following table contains output from a lasso fit to a linear model with d= 5 variables and n = 65 observations. Starting from the left, the columns are X, and B₁, ..., B5, i.e. each row has X and the transposed column vector B¹(X). 0.00000 0.00000 -0.04596 0.08497 0.04129 -0.08195 -0.00764 0.22778 -0.04274 0.07868 0.03430 -0.07599 0.00000 1.96117 -0.02092 0.04606 0.00000 -0.04090 3.28220 0.00000 0.02263 0.00000 -0.02105 4.49485 0.00000 0.00375 0.00000 0.00000 4.73846 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 You will perform computations using this table and report your results. A) Compute the maximum value of the L₁ norm for vectors of coefficients attained in this table, that is compute maxx ||3¹(A)||₁ B) Consider the 2nd breakpoint from the top of the table, namely the breakpoint corresponding to A-0.22778. Compute the L₁ norm for the vector of coefficients at this point in the path, i.e. compute || (0.22778)||1 C) For the same 2nd breakpoint in the table, compute…
8. X. Let f: RR defined by f(x) = x³ -
Suppose the function X₂+1 = (ax₂ + c) mod m is used to generate pseudo random number. Assume: m=11₁a-6,c=2, xo=5, what are x₁, x2 and x3 ?
Excel’s RAND() function generates a random number (x) such that 0 ≤ x ≤ 1. 0 < x ≤ 1. 0 ≤ x < 1. 0 < x < 1. None of the answer choices is correct.
Given a vector of real numbers r = (r1, V2, . . ., rn). We can convert this vector into a probability vector P = (P1, P2, . . ., Pn) using the formulation: p; = e¹¹/(Σï-₁ e¹¹), for all i. Write a Python function vec_to_prob(r) that takes the vector r as input and returns the vector p. Both r and p will be numpy arrays. You can assume r is non-empty. Sample inputs and outputs: Input: np.array([4, 6]), output: [0.11920292 0.88079708] • Input: np.array([3.4, 6.2, 7.1, 9.8]), output: [0.00151576 0.02492606 0.06130823 0.91224995] Hint: use numpy.sum [ ] # Write your function here Let's test your function. [ ] # Convert input from list to np.array first before calling your function to avoid errors print (vec_to_prob(np.array([4, 6]))) print (vec_to_prob (np. array ( [3.4, 6.2, 7.1, 9.8]))) print (vec_to_prob (np.array([3, 5.5, 0])))
In binomial_overbooking.xlsx, the formula in cell B7 is not general. For example, if the overbooking number is over 20, then more rows should be added to columns D to G. Write a VBA function to calculate the expected bumps. 'q:overbooking number 'n:capacity 'p: no-show probability Function binom_bump(q As Integer, n As Integer, p As Double) As Double.
Q_3 Let A be the set of all strings of decimal digits of length 5. For example 00312 and 19483 are two strings in A. You pick a string from A at random. What is the probability that the string has no 4 in it?
Generate 100 synthetic data points (x,y) as follows: x is uniform over [0,1]10 and y = P10 i=1 i ∗ xi + 0.1 ∗ N(0,1) where N(0,1) is the standard normal distribution. Implement full gradient descent and stochastic gradient descent, and test them on linear regression over the synthetic data points. Subject: Python Programming

SEE MORE QUESTIONS

Recommended textbooks for you

Operations Research : Applications and Algorithms

Computer Science

ISBN:

9780534380588

Author:

Wayne L. Winston

Publisher:

Brooks Cole

Operations Research : Applications and Algorithms

Computer Science

ISBN:

9780534380588

Author:

Wayne L. Winston

Publisher:

Brooks Cole

SEE MORE TEXTBOOKS

Write a function my_random that samples a random number from the following discrete probability distribution on the set {8, 9, 13, 15, 17, 18}: P({8}) = ²/ 9 P({9}) = ²/ 18 P({13}) = 1/ P({15}) = P({17}) = ²/ 16 NO P({18})= =