The random variable X, Y and Z have the following joint probability distribution:X11112222y11221122Z12121212f(x,y,z)0.050.100.150.200.200.150.100.05Determine the following:1. P(X=1, Y=2)2. P(Z<1.5)3.4.and Z = 2.P(X=1 or Z=2)Conditional probability distribution of X given that Y =1

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Answered: The random variable X, Y and Z have the…

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 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, y) 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 0.060 0.040 0.100 0.030 0.020 0.050 What is the probability that there is exactly one car and exactly one bus during a cycle? What is the probability that there is at most one car and at most one bus during a cycle? What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = P(exactly one bus) = - 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 overflov during a cycle?
A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course.Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 2 3 0.07 0.01 0.05 0.01 0.03 0.01 0.03 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: 1. Standard deviation of Y. 2. Fill in the blanks As the number of motorcycle drivers from Welcome Rotonda to Fairview encountered by the motorcycle (increase, decrease, or be (zero, negative, or positive) covariance. The increases, the number of stoplights of its return trip tends to uncorrelated). Therefore, X and Y have a covariance was calculated to be (numerical value). *Describe the correlation whether a strong, a weak, or no. X and Y have correlation.…
Compute the expected value for X. X 1 2 0 0.10 0.12 Y 1 0.05 0.10 2 0.02 0.16 3 0.06 0.11 0.28
The joint probability distribution of variables X and Y is shown in the table below, where X is the number of tennis racquets and Y is the number of golf clubs sold daily in a small sports store. X 1 0.13 0.08 0.22 Y 1 0.16 0.14 0.03 2 0.07 0.04 0.13 What is the expected value of X? а. 1.02 O b. 0.36 О с. 0.26 O d. 1.85
Are X and Y independent?
A motorcycle drives from Welcome Rotonda to Fairview and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Welcome Rotonda to Fairview and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by 1 2 4 0.01 0.01 0.03 0.07 0.01 0.03 0.05 0.08 0.15 1 0.03 0.02 2 0.03 0.11 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 Find: (a) Give the marginal probability distribution of fx (0). (b) Give the marginal probability distribution of fy (3). (c) Give the conditional density distribution of X=3 given Y = 3. (d) Give E(X). . (e) Give E(Y). (1) Give E(X) Y = 3). (g) Give the standard deviation of Y. *Complete the interpretation of the data. As the number of from Welcome Rotonda to Fairview encountered by the motorcycle increases, the number of stoplights of its return trip tends…
The joint distribution of the pair of random variables as given in the following table: 0 Y 1 2 -10 X 0 0.1 0.2 0.1 0 10 0.2 0 0.1 0.1 0.2 What is E(X | Y > 0)? -3.33 0.000 -4.00 3.33 -2.00 No answer
The joint probability distribution of two random variables X, Y is given in the table below. Y=-4 Y=0 Y=1_Y=4 X=-4 0.01 0.18 0.00 0.13 X=-1 0.03 0.08 0.20 0.14 X=4 0.00 0.08 0.09 0.06 From 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) = []

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