Let us assume that a turkey is classified by its weight as low, medium, or high.

Question

Let us assume that a turkey is classified by its weight as low, medium, or high. We can also assume that 3% of turkeys are classified as low, 88% as medium, and 9% as high. A sample of 20 turkeys is selected for weighing. Let X, Y, and Z represent the number of turkeys that are independently classified as low, medium, and high weight, respectively a. What are the name and values of the parameters of the joint probability distribution of the joint distribution of X, Y, and Z? 0.09,ox Tz = 1. multivariate normal; x = 0.03, = 0.88,Az multinomial; PX = 0.88,Pr = 0.09, pz = 0.03. -0.03 y multinomial; px py 0.88,pz 0.09 binomial; n-20, p-0.88 Submit Answer Tries 0/10 b. What are the name and values of the parameters of the marginal probability distribution of X? binomial; re-20, p-0.03 binomial; n = 20, p 0.88 multinomial, px = 0.03,Pr = 0.88, pz-0.09. normal; x-0.03, x 1. Submit Answer Tries 0/10 Round all answers to 4 decimal points. c. What is the expected number of medium weight turkeys?

Explanation / Answer

ANSWER :-

a)

In the given problem X ,Y and Z follows the multinomial distribution with probabilities Px = 0.03 , Py = 0.88 , Pz = 0.09

so option C is correct.

b)

The marginal probability distribution of X follows Binomial distribution with n = 20 and p = 0.03

c)

Expected value of weight of medium turkeys is

E(Y) = 20 * 0.88 = 17.6

d)

The required probability is

P(X =1 , Y=18 , Z=2) = (20! / 1!*18!*2! ) (0.03)1 (0.88)18 (0.09)2

                                       = 190 * 0.03 * 0.100 * 0.0081

                                  = 0.004617

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