1. The table below gives the joint probability mass function for X and Y. X=1 X=2| X=3 b 0.04 0.12 0.16 0.48 Y = A Y = B Suppose X and Y are independent random variables. Find a and b. a
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- The joint pdf of the random variable X and Yis given in the below matrix. Find the mean value of X and Y: P(X,Y)= X O2.45 and 2.1 O 1.9 and 2.45 O 1.9 and 2.1 O 21 and 2.45 Y 0.05 0.05 0.1 0.05 0.1 0.35 0 0.2 0.1Which of the following are a valid probability function for the given random variable? Select all that apply. 1 1 1 f(x) 1. O f(x) 1. 1. 1. 1. 2 O f(x) E) = 10 x = -1, –2, –3,-4 %3| O f(x) = x² + 1 x = 0.01, 0.02, . 0.99 ...* O f(x) = x 1 1 1 1. 2 3'6 ロf(@) x = 0,1,2, 3,4 10The joint pdf of the random variable X and Yis given in the below matrix. Find the mean value of X and Y: P(X,Y)= X O2.45 and 2.1 O 1.9 and 2.45 O 1.9 and 2.1 O 21 and 2.45 Y 0.05 0.05 0.1 0.05 0.1 0.35 0 0.2 0.1
- Suppose X and Y have the joint probability distribution given by the table shown below. Compute Cov(X,Y). -0.750 O-0.125 -0.625 -0.250 -2 y o 2 0 18 1 BIT 8 x 1 1 4 1 2 019:57 X 375 B/s A 59 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 (14 of 26) A grocery store employs cashiers, stock clerks, and deli/bakery workers. The distribution of employees with and without dependents is shown here. Dependents Cashiers Stock Clerks Deli/Bakery Workers Yes 12 3 No 5 15 2 If an employee is selected at random, find the probability that the employee is a deli/bakery worker and does have dependents. O 0.0667 O0.0444 00.1111 O 0.5111 Search inside screenshot X Share Edit Lens DeleteAssume the following data displays the joint probability for random variables X and Y: X 10 20 30 20 0.1 0.2 0.05 0.05 0.1 0.2 0.2 0.0 0.1 -1 Y O 1 1. Solve for the correlation of X and Y. 2. Solve for the correlation of X and Y conditional on Y being greater than or equal to zero. 3. Are X and Y independent? Are X and Y conditional on Y being greater than or equal to zero, independent.
- O Prove that E(X) = E(X/Y), where X and Y are two random variables which are independent. %DNeed question d and e answersFind the mean of the given probability distribution. The random variable x is the number of houses sold by a realtor in a single month Houses Sold (x) Probability P(x) at the Sendsom's Real Estate office. 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 0.11 7 0.21 Ο Α. μ-3.35 Ο Β. μ-3.60 O C. μΕ 3.40 O D. µ= 3.50
- Find the mean of the random variable Y with the given probability mass function. 1 4 p(y) .4 .2 .2 .1 .1 O 2.3 O 3 O 4.6 O 1.8 2]Consider rolling 2, 3-sided dice. Let X = the sum of the dice. Let Y = the product of the dice. a. Find the joint probability function for X and Y. b. Find the marginal probability functions for X and Y. Find P(X > 3|Y = 3) C.Show your complete solution.