The joint probability distribution of two random variables X, Y is given in the table below. Y=-3 Y=0 Y=1 X=-4 0.01 0.00 0.17 X=-3 0.21 0.19 0.02 X=4 0.22 0.05 0.13 From the information in the table, calculate each of the following three probabilities. (a) P(x < -3, Y < 0) = [] %3D (b) P(x < -5) = I (c) P(Y 2 0) = []
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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, Y is given in the table below. Y=-2 Y=0 Y=1 Y=2_Y=3 X=-3 0.17 0.00 0.04 0.04 0.12 X=-1 0.02 0.00 0.06 0.19 0.16 X=3 0.02 0.01 0.00 0.05 0.12 From the information in the table, calculate each of the following three probabilities. (a) P(Y = 2) = [ (b) P(x > -1, Y > 0) = [] (c) P(X < 3) = []The joint probability distribution of two random variables X, Y is given in the table below. Y=-3 Y=1 Y=2 X=-4 0.03 0.00 0.08 X=0 0.27 0.14 0.06 X=3 0.20 0.16 0.06 From 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) = 1 Check Explanation ALEKS - Britney Fri.
- A customs agent discovers 24 identically looking packets of white power in a traveler's suitcase. Unknown to the customs officer, 18 of these packets contain cocaine, the rest do not contain cocaine. The customs officer is to randomly pick 4 packets and test each one. A random variable X is to count the number of tested packets that test positive for cocaine. (a) Finish the probability distribution of X below. Use four decimals in each of your entries. P(X = x) 0 1 (b) From the distribution you found in part (a), what can you say about the distribution of X? E(X) 2 3 4 The distribution of X is ? SD(X) (c) How many of the 4 packets do you expect be to test positive for cocaine? Provide the standard deviation as well. (use two decimals) (use two decimals)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 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 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) •…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 joint probability distribution of two random variables X, Y is given in the table below. Y=-3 Y=2 Y=4 X=-4 0.02 0.14 0.13 X=-2 0.05 0.01 0.05 X=-1 0.09 0.00 0.11 X=1 0.12 0.15 0.07 X= 3 0.06 0.00 0.00 From the information in the table, calculate each of the following three probabilities. (a) P(Y> 2) = [ (b) P(X < 1,Y = 2) = | (c) P(Y< -3) = [] I Don't Know Submit O 2022 to search ALEKS - Britney Fri.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).Let X be a random variable with the following probability values. F(x)= c(1-2x2+x®), x= 0,1,2,3,4,5. (a) Find the value of c to make it a probability distribution. (b) Establish the probability distribution of X (table). (c) Find the mean of the random variable X.