Discrete case: In order to generate a number x from a discrete variable X ~ fx(x), letr be a random number from the uniform (0;1) distribution. Then x is the smallestfx(i) ≥ r, i.e., F(x) = r.number such that ΣASSIGNMENT: Generate 10 random numbers from the binomial (12;0,4)distribution.

The method mentioned above involves generating random numbers using the cumulative distribution…

Answered: Discrete case: In order to generate a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :
Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
2. Some properties of Expected value and variance of a random variable. a) Assume that X is an arbitrary discrete random variable, and a and b are constant. Using the definitic Show: and E(aX + b) = a · E(X) + b V(aX + b) = a² · V(X ) Stat 3128 Ali Mahzarnia P STAT 3128 Ali Mahzarnia b) Justify the computational formula of Variance of a random variable which is to justify : V(X) = E[(X – µ°] = Ex – µ)P • ptx) = | 2: Here needs justification By Cauchy Schwarz inequality it can be shown that the right hand side is always positive. Analogs expression in Mechanic : Parallel axis theorem Iem = I– md² Moment of Moment of inetria about Inertia of an an axis shifted object about the center of a mass by d from center of mass (a parallel shift) Icm is dispersion around the mean and is like second central moment (variance) I is like second moment if d is mean m is like sum total all the weight of each of the x which all add up to 1 d squared is like squared of mean since we,
A- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x= −1,1,2,3. Find the value of k. Find the Variance of X. B- Let x denote a discrete random variable which can take the values −2,0, and 5. Given that the expectation of X is 8/100 and P(X=−2)=8/20 , find P(X=5).
For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. (d) X = the length of a randomly selected rattlesnake Describe the set of possible values for the variable. 0, 1, 2, 3, ... 1, 2, 3, ... [0, ∞) (0, ∞) State whether the variable is discrete. discrete not discrete (e) Z = the sales tax percentage for a randomly selected amazon.com purchase, where n = the total number of possible sales tax percentages for online purchases Describe the set of possible values for the variable. z1, z2, z3, ..., zn [0, zn] 1, 2, 3, ..., n [0, n] State whether the variable is discrete. discrete not discrete (f) Y = the pH of a randomly chosen soil sample Describe the set of possible values for the variable. 0, 1, 2, 3, ..., 14 [0, 14] 1, 2, 3, ..., 14 (0, 14] State whether the variable is discrete. discrete not discrete (g) X = the tension (psi) at which a randomly selected…
If x is a binomial random variable, compute P(x) for each of the following cases
Let X and Y denote two random variables. Which of the following can be used to compute Var(X)? A. E[Var(X|Y)] + Var(Var(X|Y)) B. E[E[X|Y]] + Var(Var(X|Y)) C. E[Var(X|Y)] + Var(E[X|Y]) D. Var(E[X|Y]) + Var(Var(X|Y))
73
The possible values of a discrete random variable X are 0, 1, 3, and 6 with respective probabilities 0.2, 0.3, 0.1, 0.4. Find E[X] and Var(X).
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Let X1, X2, X3, X4 be independent random variables of size 4 from a gamma distribution -xª-1e-aæ with a 1a-ax G(a, X) 6 and T(a) Find the expected value of Z = X2 + X4. |3D Answer:
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y) = 4 Var(X) = 24 Var(Y) 18 Var(z)=7 E(X)= -3 E(Z) =-1 Compute the values of the expressions below. E(-4-5X)= 0 %3D ? ()- 0 Var(-3+2.X) = 0

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Discrete case: In order to generate a number x from a discrete variable X-fx(x), let r be a random number from the uniform (0;1) distribution. Then x is the smallest number such that Σ fx(i) ≥ r, i.e., F(x) = r. ASSIGNMENT: Generate 10 random numbers from the binomial (12;0,4) distribution.