The joint probability distribution of two random variables X, Y is given in the table below.Y=-4 Y=0 Y=1_Y=4X=-4 0.01 0.18 0.00 0.13X=-1 0.030.08 0.20 0.14X=40.00 0.08 0.09 0.06From the information in the table, calculate each of the following three probabilities.(a) P(Y= -4) = |(b) Р (х < -1, ү 2 0) %3D0(c) P(x< 5) = []

Answered: The joint probability distribution of…

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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The discrete random variable X has the following probability distribution: -10 0 10 p(x) 0.20 0.40 .10 Which one of the following correctly gives the value of the mean and standard deviation of X? OH = 0.5, o = 37.5 OH = 2.25, o = 37.25 OH = 0.5, o = 6.10 OH= 2.25, o = 6.10 OH= 0.5 o = 37.25
The following table gives the probability distribution of a discrete random variable x. 1 2 3 4 5 6. P(x) 0.13 0.18 0.29 0.15 0.13 0.09 0.03 Find P(x < 2).
The joint probability function of random variables X and Y is given in the table below. Show that X and Y are uncorrelated, but not independent. x = 0 2 4 y = -1 .1 .1 CamScanner 0 .1 .2 .1 1 .1 .1 .1 ECUS=
Suppose X is a discrete random variable with the following probability distribution: P(X = 2) = 0.3 P(X = 4) = 0.2 P(X = 6) = 0.5 What is the expected value (mean) of X?
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. p(x, у) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 4 0.060 0.040 0.100 0.030 0.020 0.050 (a) What is the probability that there exactly one car and exactly one bus during a cycle? (b) What is the probability that there is at most one car and at most one bus during a cycle? (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) P(exactly one bus) = (d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle? (e) Are X and Y independent rv's? Explain. Yes, because p(x, y) = Px(x) · Py(y). Yes, because p(x, y) ± Px(x) · py(y). No, because p(x, y) = Px(x) · Py(Y). No, because p(x, y) # Px(x) · Py(y).
Answer part a through d. Suppose X is normally distributed random varible with u= 15 and o=2. Find each probability.
Let X be a random variable with a mean of 20 and variance of 4. Then E(3X2 -3 X +2) is а. -46 O b. 1154 O c. 1142 O d. 1526
Find the variance for the probability distribution 4 0 1 2 3 P(X=x) 0.04 0.18 0.34 0.23 0.21 Select one: а. 1.12 b. 1.26 с. 1.59 d. 3.79
Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: 1 3 4 8 P(X = x) |0.252 0.286 0.13 0.188 0.082 0.038 0.02 0.003 0.001 a. What is the probability that a randomly selected student changed his or her major at least once? b. What is the probability that a randomly selected student changed his or her major at most twice? c. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times? (Round your answer to three decimal places.)
The joint probability distribution function of X and Y is given by: 1 2 3 1 0.05 0.06 0.10 X 2 0.13 0.21 0.30 a. Find the conditional distribution of Y given X = 1 b. Find the conditional distribution of X given Y = 2 5 0.02 0.03 0.10
Please calculate the covariance and the correlation coefficient for the two random variables and briefly comment on the resulting correlation between the variables.
Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: 1 2 3 5 6 7 8 P(X = x) 0.195 0.183 0.294 0.179 0.098 0.034 0.012 0.003 0.002 a. What is the probability that a randomly selected student changed his or her major at least once? b. What is the probability that a randomly selected student changed his or her major at most twice? c. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times? Check Answer

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