Two fair dice are rolled. Find (In tabular form) the joint and marginal probability mass functionsof X and Y when a. X is the largest value obtained on two dice and Y is the sum of the values.Compute P(Y-2X = 0); b. X is the value on the first die and Y is the larger of the two values.Compute P(Y > = X); c. X is the smallest and Y is the largest value obtained on the dice.Compute (Y > 2X). In each of three cases above, compute the joint CDF of X and Y at (sqrt(6), 2)

Here given that two fair dice are rolled. Find the joint and marginal distribution of X and Y where…

Answered: Two fair dice are rolled. Find (In…

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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A random variable x has a probability mass function defined by P(X=x) = r(x-1). if x= 2,3 r(8-x). if x=4,5,6 0. Otherwise Write out the probability mass function. What will be the expectation and variance of x. Find P (x greater or equal to 2 and less or equal to 5).
Suppose the probability function for x is such that p(x=1)=0.3, p(x=2)=0.4 and p(x=3)=0.3. What is the variance of x ?
Answer d, c, f
(32) Let X be a random variable with p.d.f. e2k x= 1,2,3 (x-1)! f(x) = , find (1) k (2) E(2x) O.w
Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).
Q2
Consider rolling 2, 3-sided dice. Let X = the sum of the dice. Let Y = the product of the dice. a. Find the joint probability function for X and Y. b. Find the marginal probability functions for X and Y. Find P(X > 3|Y = 3) C.
The table gives the joint probability distribution of the number of sports an individual plays (X) and the number of times she may get injured while playing (Y) X=1 X=2 X=3 0.12 0.08 0.15 0.06 0.05 0.05 0.10 0.03 0.15 0.15 0.04 0.02 Y=4 Y=3 Y=2 Y=1 The covariance between X and Y, oxy, is (Round your answer to two decimal places Enter a minus sign if your answer is negative) The correlation between X and Y, corr(X, Y), is (Round your answer to two decimal places Enter a minus sign if your answer is negative.) An increase in the number of sports an individual plays will tend to * the number of times she may got injured while playing
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.
In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: y 0.10 0.11 0.05 0.17 0.23 0.08 2 0.06 0.14 0.06 Find P(X = land Y = 0). a. Find P(X 2 land Y 1). b. C. d. Find the probability that the standard for ozone is exceeded at least once. Find the probability that the standard for particulate matter is never exceeded. e. f. Find the probability that neither standard is ever exceeded. g.
Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is either +1 or −1. State the conditions which make the correlation equal to +1.

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