Question

Consider the probability distribution of the discrete random vector [X,Y] where X represents the number of...

  1. Consider the probability distribution of the discrete random vector [X,Y] where X represents the number of orders for chickens in August at neighboring supermarket and Y represents the number of orders in September. The Joint distribution is showing the following table.

Y

51

52

53

54

55

51

0.06

0.05

0.05

0.01

0.01

52

0.07

0.05

0.01

0.01

0.01

53

0.05

0.10

0.10

0.05

0.05

54

0.05

0.02

0.01

0.01

0.03

55

0.05

0.06

0.05

0.01

0.03

  1. Find the probability that X ≥ 53 and Y ≥ 53 (3Marks)
  2. Find the marginal distribution of X? (2marks)
  3. Find the marginal distribution of X?(2marks)
  4. Find the expected sales for September i.e. E(Y). (3 Mark)
  5. Find P(Y≥53 | X =55)       
  6. Calculate the correlation coefficient of X and Y (6Marks)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the following bivariate distribution p(x, y) of two discrete random variables X and Y. Y\X...
Consider the following bivariate distribution p(x, y) of two discrete random variables X and Y. Y\X -2 -1 0 1 2 0 0.01 0.02 0.03 0.10 0.10 1 0.05 0.10 0.05 0.07 0.20 2 0.10 0.05 0.03 0.05 0.04 a) Compute the marginal distributions p(x) and p(y) b) The conditional distributions P(X = x | Y = 1) c) Are these random variables independent? d) Find E[XY] e) Find Cov(X, Y) and Corr(X, Y)
Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets....
Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying table. y 45 46 47 48 49 50 51 52 53 54 55 p(y) 0.05 0.10 0.12 0.14 0.25 0.17 0.05 0.02 0.06 0.01 0.03 Calculate V(Y) and σY. (Round your variance to four decimal places...
Consider joint Probability distribution of two random variables X and Y given as following f(x,y)   X...
Consider joint Probability distribution of two random variables X and Y given as following f(x,y)   X        2   4   6 Y   1   0.1   0.15   0.06    3   0.17   0.1   0.18    5   0.04   0.07   0.13 (a)   Find expected value of g(X,Y) = XY2 (b)   Find Covariance of Cov(x,y)
Problem 3. Let x be a discrete random variable with the probability distribution given in the...
Problem 3. Let x be a discrete random variable with the probability distribution given in the following table: x = 50 100 150 200 250 300 350 p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10 (i) Find µ, σ 2 , and σ. (ii) Construct a probability histogram for p(x). (iii) What is the probability that x will fall in the interval [µ − σ, µ + σ]?
In the accompanying​ table, the random variable x represents the number of televisions in a household...
In the accompanying​ table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability​ distribution, find its mean and standard deviation. x   P(x) 0   0.03 1   0.13 2   0.32 3   0.25 4   0.17 5   0.10 If the table is a probability​ distribution, what is its​ mean? Select the correct choice below and fill in any answer boxes within your...
The probability distribution of a couple of random variables (X, Y) is given by : X/Y...
The probability distribution of a couple of random variables (X, Y) is given by : X/Y 0 1 2 -1 a 2a a 0 0 a a 1 3a 0 a 1) Find "a" 2) Find the marginal distribution of X and Y 3) Are variables X and Y independent? 4) Calculate V(2X+3Y) and Cov(2X,5Y)
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) =...
X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) = 1/5(y+2) , 0 < y < 1, y-1 < x < y +1 = 0, otherwise a) Find marginal density of Y, fy(y) b) Calculate E[X | Y = 0]
Create the probability distribution for a random variable X that represents the following:The number of girls...
Create the probability distribution for a random variable X that represents the following:The number of girls in a 3 child family.
If the joint probability distribution of X and Y is given by: f (x, y) =...
If the joint probability distribution of X and Y is given by: f (x, y) = 3k (x + y), for x = 0, 1, 2, 3; y = 0, 1, 2. a) .- Find the constant k. b) .- Using the table of the joint distribution and the marginal distributions, determine if variable X and variable Y are independent.
The joint probability distribution of two random variables X and Y is given in the following...
The joint probability distribution of two random variables X and Y is given in the following table X Y → ↓ 0 1 2 3 f(x) 2 1/12 1/12 1/12 1/12 3 1/12 1/6 1/12 0 4 1/12 1/12 0 1/6 f(y) a) Find the marginal density of X and the marginal density of Y. (add them to the above table) b) Are X and Y independent? c) Compute the P{Y>1| X>2} d) Compute the expected value of X. e)...