The solution to problem 1 a) . Page 2 of 3 Problem 1 Find the correct answer to
ID: 3313159 • Letter: T
Question
The solution to problem 1a).
Page 2 of 3 Problem 1 Find the correct answer to each question. The calculation does not need to be included. a) Let X be a discrete random variable with probability mass function as given in the table below PX )0.4 0.3 0.2 0.1 what is P(X = 3]X 2 1)? A) 0.13 B) 0.17 C) 0.1 D) 0.33 E) balls and 5 blue balls. What is the probability that two balls are red and one ball is b) Three balls are drawn at random (without replacement) from a box containing 5 red blue? A) 0.76 B) 0.08 C) 0.73 D) 0.42 E)0.86 c) Suppose that a test statistic X is normally distributed with mean and standard de- 0 has acceptance region viation 1 and that the test of H: = 0 versus H1 : (-1.96, 1.96). If = 3, the power of the test will be A) 0.05 B) 0.33 C) 0.95 D) 0.80 B)0.85 d) The prevalence of a disease is 1 in 10, and there is a test that can detect it with a sen- tivity of 85% and a specificity of 81% what is the probability that a person has the disease, given a negative result on the test? A) 0.1 B) 005 C) 0.15 D) 0.08 ) 0.02Explanation / Answer
1 a)
P(X=3 / X>=1) = P(X=3 and X>=1) / P(X>=1)
= P(X = 3) / P(X>=1)
=0.1 / [0.3+0.2+0.1] = 0.1 / 0.6 = 0.16667
Correct answer: Option (B) 0.17