4.73 consider the joint probability distribution - Compuut We mean and variance for the leaf function...
EXERCISE 2.21 The joint probability distribution of the size of a company's sales force and its yearly sales revenue is as shown in Table 2.32. (a) Compute the mean, variance, and the standard deviation of the size of the sales force (b) Compute the mean, variance, and the standard deviation of yearly sales revenue. (c) Compute the covariance and correlation of the size of the sales force and yearly sales revenue. Probability Number of Sales People Yearly Sales Revenues (S100,000)...
The following table presents the joint probability mass function pmf of variables X and Y 0 2 0.14 0.06 0.21 2 0.09 0.35 0.15 (a) Compute the probability that P(X +Y 3 2) (b) Compute the expected value of the function (X, Y)3 (c) Compute the marginal probability distributions of X and )Y (d) Compute the variances of X and Y (e) Compute the covariance and correlation of X and Y. (f) Are X and Y statistically independent? Clearly prove...
The following joint probability distribution is given. 1. Find k such that the given function demonstrates the PDF. 2. Find Marginal distributions. 3. Evaluate ?(? < ? < 0) 4. Find the correlation coefficient between X and Y having the joint density functions:(.) ?(?,?) = {???2+?2 ??? ?2 + ?2 < 4 0 ?????h??? Question 2. (20 pts.) The following joint probability distribution is given. 1. Find k such that the given function demonstrates the PDF. 2. Find Marginal distributions....
Use the probability distribution given in the table below and consider two new random variables, W= 1 + 9X and V = 4 + 2Y, to answer the following questions Joint Distribution of Weather Conditions and Commuting Times Long commute (Y = 0) Short commute (Y = 1) Total Rain (X = 0) 0.04 0.50 0.54 No Rain (X = 1) 0.32 0.14 0.46 Total 0.36 0.64 1.00 Compute the mean of W. E(W) = (Round your response to two...
Question Use the probability distribution given in the table below to answer the following questions Joint Distribution of Weather Conditions and Commuting Times Rain (X 0) No Rain (X 1) Total Long commute (Y 0) Short commute (Y 1) 0.26 0.13 0.39 0.58 0.03 0.61 Total 0.84 0.16 1.00 Compute the mean of Y E (Y) (Round your response to two decimal places) Compute the mean of X E (X) (Round your response to two decimal places) Compute the variance...
The following table gives the joint probability distribution between employment status and college graduation among those either employed or looking for work (unemployed) in the working-age U.S. population for 2016. | Unemployed (Y = 0) . Employed (Y = 1) Non-college graduates (X- 0 College graduates (X 1) 0.045 0.026 0.621 0.308 (a) Compute the expected value (mean) of X and Y: E(X), E(Y). (b) Compute the variance of X and Y: ơ (c) Compute the covariance and correlation coefficient:...
1 * Consider the following joint distribution for the weather in two consecutive days. Let X and Y be the random variables for the weather in the first and the second days, whereas the weather is coded as 0 for sunny, 1 for cloudy, and 2 for rainy. 0 0.2 0.2 0.2 10.1 0.1 0.1 2 0 0.1 0 (a) Find the marginal probability mass functions for X and Y (b) Are the weather in two consecutive days independent? (c)...
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
Please show how did you came up with the answer, show formulas and work. Also, please do Parts e to i. Thank you so much 1. Consider the following probability mass function for the discrete joint probability distribution for random variables X and Y where the possible values for X are 0, 1, 2, and 3; and the possible values for Y are 0, 1, 2, 3, and 4. p(x,y) <0 3 0 4 0.01 0 0 0.10 0.05 0.15...