Show all the work. Give numerical values to all probabilities Two identical but
ID: 3357377 • Letter: S
Question
Show all the work. Give numerical values to all probabilities Two identical but not ordinary dice are rolled. Each die has only four faces with numbers 1, 6, 7, and 10. Let X be the sum of the two numbers. Construct the PMF of X 1. f(x) 2. A random sample of three numbers is selected from the numbers 1, 2,3, 4,... 10. Let X be the smallest of the three numbers. Give the PMF of X as a table or a formula. Find E(X) and 2. a. b. 3. A test for the presence of antibodies to the AIDS virus in blood has probability 0.98 of detecting the antibodies when they are present. Suppose we test eight units of blood with AIDS antibodies. Let X be the number of contaminated units detected by the test. a. Give a formula for the PMF of X As a lab technician, would you be surprised if you find out that the tests you had just performed detected only five of the eight contaminated units? Use probabilities to justify your answer. b.Explanation / Answer
Question 1:
Here for the 2 dice the sum on the 2 faces is computed for each of the 16 combinations as:
From the above combinations, the PDF for X here which is the sum on the 2 dice is computed as:
This is the required PDF for X here.
Sum K = 1 K = 6 K = 7 K = 10 Y = 1 2 7 8 11 Y = 6 7 12 13 16 Y = 7 8 13 14 17 Y = 10 11 16 17 20