The joint probability distribution of two random variables X, Y is given in the table below.Y=-3 Y=1 Y=2X=-40.030.00 0.08X=00.270.14 0.06X=30.200.16 0.06From the information in the table, calculate each of the following three probabilities.(a) P(X> -4) = [(b) P(Y = 2) = [](c) P(X > 0.Y < 1) = 1CheckExplanationALEKS - Britney Fri.

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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 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 distribution of two random variables, X and Y, is given in the table below. Y=-3 Y=1 Y=3 Y=4 X=-4 0.15 0.01 0.00 0.17 X=-1 0.12 0.04 0.13 0.00 X=2 0.01 0.18 0.00 0.19 From the information in the table, calculate each of the following probabilities. Round your answers to two decimal places. (If necessary, consult a list of formulas.) (a) Given that X=-1, compute the probability that Y= 1. (b) Given that X> -1, compute the probability that Y<3. Explanation Check ALEKS - Britney Fri.
The probability distribution of random variable X is given as follow: 2 3 4 5 f (x) 0.41 0.37 0.16 0.05 0.01 0.00 Find the mean of X? E(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).
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. y 1 p(x, y) 0 1 0.030 0.020 50 X 3 0.090 0.060 4 0.060 0.040 2 0 0.015 0.010 0.025 0.050 2 0.075 0.050 0.125 0.150 0.100 5 0.030 0.020 0.050 (a) What is the probability that there is exactly one car and exactly one bus during a cycle? 0.020 (b) What is the probability that there is at most one car and at most one bus during a cycle? 0.075 (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = 0.220 x P(exactly one bus) = 0.200 (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? 0.985 X (e) Are X and Y independent rv's? Explain. O Yes, because p(x, y) = P(x) Py(Y). O Yes, because p(x, y) = Px(x) • P₂(Y). # ● No, because p(x, y) = Px(x) •…
2
The probability distribution for the random variable, x, is x:2, 2.5,3.0,3.5,4.0 ,4.5 and P(x):0.07, 0.36, 0.21, 0.19, 0.10, 0.07 Calculate P(x >= 3.0) a. 0.57 O b. 0.19 O C. 0.83 d. 0.47 O
Find P(X=1 and X=2) Refer to the probability function given in following table for a random variable X that takes on the values 1,2,3 and 4 X 1 2 3 4 P(X=x) 0.4 0.3 0.2 0.1
The annual premium for a $15,000 insurance policy against the theft of a painting is $250. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Let X be the random variable for the amount of money received from the insurance company in the given year. E(X)= dollars
The following table represents the joint probability distribution of the number of people waiting in line at Food Truck X and Food Truck Y. Y=0 Y=1 Y=2 Y=3 PX(X=x) X=0 0.32 0.06 0.025 0.01 X=1 0.02 0.05 0.07 X=2 0.025 0.05 0.105 X=3 0.026 0.2 0.05 0.024 PY(Y=y) 0.114 a. Determine the probability of 3 people waiting in line at Food Truck Y and 2 people waiting in line at Food Truck X. b. What is the probability of at most 3 people waiting in line at both Food Truck X and Y combined? c. If at least 2 people are waiting in line at Food Truck X, what is the probability that 3 people are waiting in line at Food Truck Y?
Let X be a binomial random variable. If E(X)=3 and V(X)=1.5, then p(X=2) equals 0.234 0.016 0.156 0.547
Let Y be a random variable with the following probability distribution: p(y) = y/6 for y = 1; 2; 3 and (0 otherwise). Write the probability distribution for Y in the form of a table. Find E(Y), V(Y), and E(Y 3 − 1).

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