Question

Let X be the number of times a certain numerical control machine will malfunction on a given dy and Y be the number of times a technician is called on an emergency call. Their joint pr bability mass function is given by Y 10 20 30 40 15 k 0.01 k 0.02 30 0.05 k 0.02 k 45 0.1 0.05 0.03 0.12 50 0.2 0.15 0.06 0.15 Compute the constant k and determine the followings: a) Marginal distribution of X. b) Marginal distribution of Y. c) Conditional distribution of X given the value of Y = 30. d) Conditional distribution of Y given the value of X = 30.

Answer 1

To find the constant k, we add up all the probabilities in the joint probability mass function and set the sum equal to 1. Solving for k, we find that k = 6.67.

Step-by-step explanation:

To find the constant k, we need to use the fact that the sum of all probabilities in a joint probability mass function is equal to 1. So we add up all the probabilities given and set the sum equal to 1:

0.01k + 0.02k + 0.05 + 0.02k + 0.1 + 0.05 + 0.03 + 0.12 + 0.2 + 0.15 + 0.06 + 0.15 = 1

Combining like terms, we get:

0.06k + 0.6 = 1

Subtracting 0.6 from both sides, we have:

0.06k = 0.4

Dividing both sides by 0.06, we get:

k = 6.67