3. Problem 3: Assume that the joint probability of X (receive values 1, 2)and Y (receives values 1, 2, 3) is represented by the following tableY123X10.140.42 0.060.060.28 0.04• Are X and Y independent?Compute E(X +Y) and E(XY).

Answered: Image /qna-images/answer/1e45c2ce-d27a-4966-801a-a29583e63175.jpg

Answered: 3. Problem 3: Assume that the joint…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1. A contractor is required by a county planning department to submit one, two, three, or four forms (depending on the nature of the project) in applying for a building permit. Let X be the number of forms required of the next application. The probability that x forms are required is proportional to x. That is, f(x) = cx for x = 1,2,3,4. [8 points] a. Find the value of c so that f(x) is a legitimate probability mass function (pmf). b. How many forms would be expected to be required of the next application on average? c. Find the probability that at most 2 forms are required.
1.Suppose that one word is to be selected at random from the sentence "THE GIRL PUT ON HER BEAUTIFUL RED HAT". If X denotes the number of letters in the word that is selected, (1) What is the value of E(X)? (2) What is the value of Var(X)?
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aanswer:
1. Random variable X has p.d.f -6z 6e fx(z) otherwise and let Y = eX. Calculate E(X)
3. Suppose X is a discrete random variable with pmf defined as p(x) = log10 ( for %3D x = {1,2,3,...9} Prove that p(x) is a legitimate pmf.
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
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3. Problem 3: Assume that the joint probability of X (receive values 1, 2) and Y (receives values 1, 2, 3) is represented by the following table Y 1 2 3 X 1 0.14 0.42 0.06 0.06 0.28 0.04 • Are X and Y independent? Compute E(X +Y) and E(XY).