Problem 1 a. A random variable, X, is uniform, a box from 0 to 1 of height 1. (S

Question

Problem 1 a. A random variable, X, is uniform, a box from 0 to 1 of height 1. (So that its density is f(r) 1 for 0 zsi) What is its median? b. Consider the following random variable and probability mass function X {2, 3, 4, 5) P(X 5) 0.4 What is the variance of X? Problem 2 An airline knows that 5 percent of the people making flight from San reservations on a Diego to Oakland will not show up. Consequently, their policy is 52 a to sell tickets for flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger that shows up? Problem 3 A website for home pregnancy test cites the following: "When the subjects using the test were women who collected and tested their own samples, the overall sensitivity was 75%. The specificity2 was 52%. Suppose a subject has a positive test and that 30% of women taking pregnancy tests are actually pregnant. [1] Sensitivity: probability that the test is positive given that the subject is pregnant. (2 Specificity: probability that the test is negative given that the subject is not pregnant. What is the probability of pregnancy given a positive test? Problem 4 (Chapter 12.5, #3)

Explanation / Answer

Problem 1:

a)X is a random variable following uniform distribution between 0 to 1 . We need to find out median. Since, it follows uniform distrution throughout its median is equal to mean

so we have mean of X = E(X) for X following uniform distribution between a and b is (a+b)/2 = (0 + 1)/2 = 1/2

b)Variance of X = E(X^2) - [E(X)]^2

E(X) = 2*0.1 + 3*0.2 + 4*0.3 + 5*0.4

=4

E(X^2) = 4*0.1 + 9*0.2 + 16*0.3 + 25*0.4 =17

Hence variance of X = 17-4^2 = 17-16=1

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