- Information
- AI Chat
Stats 3y03 assignment 3
Probability and Statistics for Engineering (Stats 3Y03)
McMaster University
Recommended for you
Preview text
STATS 3Y03 Assignment
Problem #1: Suppose that the random variable X has the following cumulative distribution function.
0 x < 4
F ( x ) = ( x 2 − 16)4 ≤ x < 9
1 x > 9
(a) Find P ( X > 4) (b) Find P (3 < X < 4) (c) Find the mean of X. (d) Find the variance of X.
Correct Answer: 0. Problem #1(a): 0. Your Mark: 1/ Correct Answer: 0. Problem #1(b): 0. Your Mark: 1/ Correct Answer: 266/ Problem #1(c): 6. Your Mark: 1/ Correct Answer: 6025/ Problem #1(d): 1. Your Mark: 1/
Problem #1 Attempt #1 Attempt #2 Attempt # Your Answer: 1(a) 0. 1(b) 0. 1(c) 6. 1(d) 1.
1(a) 1(b) 1(c) 1(d)
1(a) 1(b) 1(c) 1(d)
{
Your Mark: 1(a) 1/1 ✔ 1(b) 1/1 ✔ 1(c) 1/1 ✔ 1(d) 1/1 ✔
1(a) 1(b) 1(c) 1(d)
1(a) 1(b) 1(c) 1(d)
Problem #2: An 1868 paper by German physician Carl Wunderlich reported, based on over a million body temperature
readings, that healthy adult body temperatures are approximately normally distributed with mean 98 degrees Farenheit and standard deviation 0.
(a) Based on this study, what percentage of healthy adults have a body temperature that is below 98 degrees? (b) Fill in the blank. Approximately 90% of healthy adults have a body temperature that is above ________ (how many?) degrees.
NOTE: Do not use the first half of the normal table (i., page 742 in the textbook, with negative z -values) because it will not be provided with the tests.
Enter your answer as a percentage , correct to 2 decimals , without the % sign. e., 28. Problem #2(a): 25. Correct Answer: 25. Your Mark: 1/ answer correct to 2 decimals Problem #2(b): 97 Correct Answer: 97. Your Mark: 1/ Problem #2 Attempt #1 Attempt #2 Attempt # Your Answer: 2(a) 25. 2(b) 97.
2(a) 2(b)
2(a) 2(b) Your Mark: 2(a) 1/1 ✔ 2(b) 1/1 ✔
2(a) 2(b)
2(a) 2(b)
Your Answer: 5(a) 0. 5(b) 498.
5(a) 5(b) 497.
5(a) 5(b) Your Mark: 5(a) 1/1 ✔ 5(b) 0/1✘
5(a) 5(b) 1/1 ✔
5(a) 5(b)
Problem #6: Suppose that the random variables X and Y have the following joint probability density function.
f ( x , y ) = ce −7 x − 9 y , 0 < y < x.
(a) Find the value of c.
(b) Find P ( X < , Y < 2) Correct Answer: 112 Problem #6(a): 112 Your Mark: 1/ Correct Answer: 0. Problem #6(b): 0. Your Mark: 1/ Problem #6 Attempt #1 Attempt #2 Attempt # Your Answer: 6(a) 63 6(b) 0.
6(a) 112 6(b) 0.
6(a) 6(b) Your Mark: 6(a) 0/1✘ 6(b) 0/1✘
6(a) 1/1 ✔ 6(b) 1/1 ✔
6(a) 6(b)
Problem #7: Suppose that the random variables X and Y have the following joint probability density function.
7 9
f ( x , y ) = ce −7 x − 9 y , 0 < y < x.
(a) Find P ( X < 2, Y < ).
(b) Find the marginal probability distribution of X.
Correct Answer: 0. Problem #7(a): 0. Your Mark: 1/ Do not include the range for x
Problem #7(b): ( e −7 x )(1 − e −9 x ) ( Correct Answer: which is x > 0). ( e −7 x )(1 − e −9 x ) Your Mark: 1/ Problem #7 Attempt #1 Attempt #2 Attempt # Your Answer: Your Mark:
7(a) 0. 7(b) ( e −7 x )(1 − e −9 x )
7(a) 0/1✘ 7(b) 1/1 ✔
7(a) 0. 7(b) 7(a) 0/1✘ 7(b)
7(a) 0. 7(b) 7(a) 1/1 ✔ 7(b)
Problem #8: Suppose that X and Y have the following joint probability density function.
f ( x , y ) = y , 0 < x < 6, y > 0, x − 2 < y < x + 2
(a) Find E ( XY ). (b) Find the covariance between X and Y.
Correct Answer: 18. Problem #8(a): 18. Your Mark: 1/ Correct Answer: 1.
Problem #8(b): 1. Your Mark: 1/ Problem #8 Attempt #1 Attempt #2 Attempt # Your Answer: 8(a) 17. 8(b) 2.
8(a) 18. 8(b) 1.
8(a) 8(b) Your Mark: 8(a) 0/1✘ 8(b) 0/1✘
8(a) 1/1 ✔ 8(b) 1/1 ✔
8(a) 8(b)
Problem #9: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the
loads is a 1 X 1 + a 2 X 2.
Suppose that X 1 and X 2 are independent random variables with means 3 and 8 kips, respectively, and standard deviations 0 and 1 kips, respectively. Suppose that a 1 = 5 ft and a 2 = 12 ft.
(a) Find the expected value of the bending moment. (b) Find the standard deviation of the bending moment. (c) If X 1 and X 2 are normally distributed, what is the probability that the bending moment will exceed 140 kipft?
Correct Answer: 111 Problem #9(a): 111 Your Mark: 1/ Problem #9(b): 18 Correct Answer: 18.
Your Mark: 1/ Correct Answer: 0. Problem #9(c): 0. Your Mark: 1/ Problem #9 Attempt #1 Attempt #2 Attempt # Your Answer: 9(a) 111 9(b) 18. 9(c) 0.
9(a) 9(b) 18. 9(c)
9(a) 9(b) 9(c)
Your Mark: 9(a) 1/1 ✔ 9(b) 0/1✘ 9(c) 1/1 ✔
9(a) 9(b) 1/1 ✔ 9(c)
9(a) 9(b) 9(c)
Stats 3y03 assignment 3
Course: Probability and Statistics for Engineering (Stats 3Y03)
University: McMaster University
This is a preview
Access to all documents
Get Unlimited Downloads
Improve your grades
