The joint probability distribution of two random variables X, Y is given in the table below. Y=-4 Y=-2 Y=0 Y=2 Y = 4 X=0 0.02 0.07 0.11 0.03 0.08 X=2 0.00 0.11 0.09 0.12 0.00 X=3 0.19 0.05 0.00 0.03 0.10 From the information in the table, calculate each of the following three probabilities. (a) P(X<2, Y≥-2)-0 (b) P(x < 0) = (c) P(X<3)= X Ś

Let E and F be two events of an experiment where P(E) = 0.45, P(F) = 0.12 and P(EnF) = 0.04. Then P(EUF) Select one: O a. 0.96 O b. 0.484 O c. 0.3333 O d. 0.946 e. 0.054

Let Y be negative binomial random variable with r=2 and p=0.4, then find E(Y²) 15 None 67.5 32.5 20

D. In panel data, there are two key models, REM and FEM. Explain what the two models are, stating their key assumptions, differences, advantages and disadvantages.

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 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

Fill in the P=Xx values to give a legitimate probability distribution for the discrete random variable X , whose possible values are −4, −3, −2, 5, and 6. ValuexofX P=Xx −4 0.23 −3 0.19 −2 0.30 5   6

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

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.

Construct the marginal probability distribution of Y. What is the mean of X and Y .