If two balanced dice are rolled simultaneously, X₂ is theappearance of one side on the first die, and X₂ representsthe number of appearances on both sides of the diea Find the joint probability mass function (tmp),PCX₁ = X₁₁ X₂ = X/₂₁ ) !b Find the marginal probability mass function foreach of the variables X₁ and X₂!

a) The possible values of x1 are 1, 2, 3, 4, 5, 6, and the possible values of x2 are 0, 1, 2. To…

Answered: If two balanced dice are rolled…

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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There are two varieties of cucumbers - C1 and C2 which have different distributions of length. The joint probability density function of the length of the cucumber and category 1 is denoted by p(x, C1), and is a uniform distribution over the range (10cm, 30cm). Similarly p(x, C2) is a uniform distribution over the range (20cm, 50cm). What is the error of classification we will make if we assert that all cucumbers of length less than 25cm are of Variety C1 and all cucumbers of length greater than 25cm are of Variety C2?.
The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…
A person’s body temperature follows a uniform distribution and can be anywhere in the range of 95 °to 106 °for a living person Draw the graph of the density curve. What is the probability that a person’s body temperature will be more than 98°? What is the probability that a person’s body temperature will be between 97°and 99°? What is the probability that a person’s body temperature will be below 100°?
9. The random variable X has probability density function, f(x) where k 1
A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.
Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce-8x - 5y, 0 0).

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