Consider the joint probability distribution of car ownership (X) and number of household members (Y) as...
ka (3) [6 pts] X and Y are discrete random variables with the following joint distribution: 14 22 30 065 102 0.05 0.10 0.03 0.01 Value ofX 50.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 (a) Calculate the probability distribution, mean, and variance of Y (b) Calculate the prohability distribution, mea, and variane of Y given X (c) Calculate the covariance and correlation between X and Y 8
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 p(x, y) 0 1 2 x 0 0.025 0.010 0.015 1 0.050 0.020 0.030 2 0.125 0.050 0.075 3 0.150 0.060 0.090 4 0.100 0.040 0.060 5 0.050 0.020 0.030 (a) What is the probability that there is exactly one car and exactly one bus during...
Recent research suggests that car ownership may have peaked. The following probability distribution table shows the random variable, x, where x is number of cars owned by household: x p (x) 0 0.10 1 0.27 2 0.40 3 0.18 4 0.05 Determine the mean of x. (b) Determine the standard deviation of x.
Assume we choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Here is the probability model if we ignore the few households that own more than five cars. Cars (X) 0 1 2 3 4 5 P(X) 0.09 0.36 0.35 0.13 0.05 0.02 Suppose the cost of gas plummets and the price of cars drastically drops, so that every household purchases an additional 3 cars,...
Given the following joint distribution of two random variables X
and Y
(a) Compute marginal distribution PX(x)
(b) Compute marginal distribution PY(y)
(c) What is the conditional probability P(Y | X = 2)?
20.10 0.05 0.15 0.10 0.10 4 0.04 0.02 0.06 0.04 0.04 6 0.04 0.02 0.06 0.06 0.02 8 0.02 0.01 0.03 0 0.04
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
Using the joint probability table below, determine P(X=0 [Y=5). 3 х 10 0.05 0.15 0.05 1 10.15 0.3 0.15 Y 1 0 0.05 0.1 5 7 a. 0.75 b.0.35 C. 0.15 d. 0.03 e. 0.3
Q1. [4+2+4 marks] Consider the following joint probability distribution fxy(x, y). 2 4 0.05 0.1 0,05 0.02 0.1 0.05 2 0.02 0.13 0.3 0.01 0.02 0.15 a) Find the covariance between X and Y b) Are X and Y independent? Explain. c) Find V(X12).
Recent research suggests that car ownership may have peaked. The following probability distribution table shows the random variable, x, where x is number of cars owned by household: x p(x) 0 .10 1 .27 2 .40 3 .18 4 .05 Determine the mean of x (Round the answer to two decimal places). . (b) Determine the standard deviation of x. (Round the answer to two decimal places)