Math 128 – Exam #2 Questions – Spring 2015
1.) Let 𝑝(𝑥) = 𝑘(𝑥+1)5 be a PDF for 0 ≤ 𝑥 2
(B) 𝐹(𝑥) = {1−𝑥2 0 ≤ 𝑥 ≤ 21 𝑥 > 2
(C) 𝐹(𝑥) = {𝑥 −14𝑥2 0 ≤ 𝑥 ≤ 21 𝑥 > 2
(D) 𝐹(𝑥) = {𝑥 −14𝑥2 0 ≤ 𝑥 ≤ 20 𝑥 > 2
Math 128 – Exam #2 Questions – Spring 2015
3.) Suppose X is a random variable whose PDF has the graph in #2. Calculate𝑃(𝑋 ≤ 1).
(A) 34 (B) 58 (C) 1116 (D) 78
4.) Suppose X is a random variable whose CDF is given by:
𝐹(𝑥) = {0 𝑥 1}
The mean for this random variable is
(A) 0.79 (B) 0.50 (C) 0.75 (D) 0.63
5.) Using the CDF in question #4, calculate the median of this distribution:
(A) 0.79 (B) 0.50 (C) 0.75 (D) 0.63
6.) Suppose X is a random variable with an exponential distribution on 0 ≤ 𝑥 ≤ ∞ with a PDF
𝑝(𝑥) = 0.25𝑒−0.25𝑥. Then the median for X is:
(A) 4.00 (B) 3.21 (C) 2.77 (D) 0.17
7.) The CDF for the random variable in question #6 on 0 ≤ 𝑥 ≤ ∞ is which of the following:
(A) 𝑒−0.25𝑥 +1
(B) 𝑒−0.25𝑥 − 1
(C) −𝑒−0.25𝑥
(D) 1−𝑒−0.25𝑥
8.) Suppose an insurance company sells an auto accident policy and determines the claims on
this policy have an exponential distribution with pdf 𝑝(𝑥) = 0.67𝑒−0.67𝑥 where 𝑥 is measured in
thousands of dollars. What is the average claim on this policy for someone who makes a claim?
(A) $1,200 (B) $1,500 (C) $1,800 (D) $2,000
9.) The speeds of cars on a crowded interstate highway are approximately normally distributed
with a mean 𝜇 = 55 mph and a standard deviation of 𝜎 = 10 mph. What fraction of the cars are
traveling between 50 mph and 65 mph?
(A) 0.53 (B) 0.38 (C) 0.49 (D) 0.61
Math 128 – Exam #2 Questions – Spring 2015
10.) If X is normally distributed with a mean of 800 and a standard deviation of 150. Compute
𝑃(725 ≤ 𝑋 ≤ 1100).
(A) 0.29 (B) 0.67 (C) 0.48 (D) 0.59
11.) Suppose X is a random variable with PDF
𝑝(𝑥) = {
0 𝑥 < 2
2𝑥2 𝑥 ≥ 2
Calculate 𝑃(𝑋 ≥ 4).
(A) 0.25 (B) 0.50 (C) 0.75 (D) 0.67
12.) Calculate 𝑓𝑥𝑦(2,3) for 𝑓(𝑥,𝑦) = (𝑥𝑦)2 + 𝑥𝑦
(A) 2559 (B) 179 (C) 2289 (D) 2389
13.) If 𝑓(𝑥,𝑦) = 𝑒𝑥2+𝑦, calculate 𝑓𝑥𝑥
(A) 2𝑒(𝑥2+𝑦)(1+2𝑥2)
(B) 2𝑒(𝑥2+𝑦)
(C) 4𝑥𝑒(𝑥2+𝑦)
(D) 𝑒(𝑥2+𝑦)(4+ 𝑥)
(E) None of these
14.) 𝑓(𝑥,𝑦) = 𝑥2 +3𝑥𝑦 +𝑦3 represents a surface. When𝑦 = 3, 𝑓(𝑥,3) is a curve on this
surface, determine the rate of change of 𝑓 along this curve when 𝑥 = 2.
(A) 4 (B) 8 (C) 10 (D) 13
15.) Let 𝑓(𝑥,𝑦) = 𝑥3 −3𝑥𝑦2 + 6𝑦+ 10. Find the critical values of 𝑓.
(A) (1,−1)
(B) (1,1),(−1,−1)
(C) (1,1),(−1,1),(1,−1)
(D) (1,−1), (−1,1), (1,1), (−1,−1)