In a far away and long ago, there are only two weather states, rain and sun. If it's sunny today the probability it's be sunny tomorrow is 0.8. If it's rainy today the probability it'll be sunny tomorrow is 0.4. Weather changes are well described by a Markov chain. a) It's sunny today, and tomorrow is the start a 4-day holiday. What is the probability that all 4 days are sunny? b) A parade scheduled for the last day of the holiday. What is the probability of rain on the parade? c) A royal wedding is planned for one year (365) from today. If it's an outdoor wedding what is the probability the wedding gets rained out.
Hint: This is the steps. Thank you
n a land far away and long ago, there are only two weather states, rain and sun. If it's sunny today the probability it'll be sunny tomorrow is 0.8. If it's rainy today the probability it'll be sunny tomorrow is 0.4. Weather changes are well described by a Markov chain. (a) It's sunny today, and tomorrow is the start a 4 - day holiday. What is the probability that all 4 days are sunny? (b) A parade scheduled for the last day of the holiday. What is probability of rain on the parade? (c) A royal wed ding is planned for one year (365 days) from today. If it's an outdoor wedding what is the probability the wedding gets rained out
In: Statistics and Probability
4.4/7.
7.The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts (a) and (b) below. Are these events unlikely?
_ No_(Did_Not_Lie) Yes_(Lied)
Positive_test_result 9 22
Negative_test_result 40 15
a. Four of the test subjects are randomly selected with replacement, and they all had true negative test results.
b. Four of the test subjects are randomly selected without replacement, and they all had true negative test results.
a. The probability that all four test subjects had a true negative test result when they are randomly selected with replacement is
(Round to three decimal places as needed.)
Is such an event unlikely?
Yes, because the probability of the event is greater than 0.05
No, because the probability of the event is greater than 0.05
Yes, because the probability of the event is less than 0.05
No, because the probability of the event is less than 0.05
B. The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is____
(Round to three decimal places as needed.)
Is such an event unlikely?
Yes, because the probability of the event is greater than 0.05
No, because the probability of the event is greater than 0.05
Yes, because the probability of the event is less than 0.05
No, because the probability of the event is less than 0.05
In: Statistics and Probability
Suppose the price of one typical stock could only increase by 2 or decrease by 1 in one day. From the historical data, we somehow know that this stock goes up with probability 0.7, goes down with probability 0.3. Suppose the initial price is 100. Suppose we want to study the price behavior for that stock for one week(5-weekdays). (Round your answer in 3 decimal Places) This question is just for setting up the model.
what is the probability of the stock price close up at 102 at the end of Monday?
what is the probability of the stock price close up at 99 at the end of Monday?
Which of the following distribution bear the most resemblance to the distribution of stock price on Monday?
what is the probability of the stock price close up at 107 at the end of Friday?
Which of the following distribution bear the most resemblance to the distribution of stock price at the end of Friday?
what is the probability of the stock price close up at 108 at the end of Friday?
what is the probability of the stock price close up at most as 107 (include 107 itself) at the end of Friday?
what is the probability of the stock price close up at least as 108 (include 108 itself) at the end of Friday?
what is the probability of the stock price close up at least as 107 (include 107 itself) at the end of Friday?
what is the probability of the stock price close up at most as 100 (include 100 itself) at the end of Friday?
In: Finance
The textbook basically says that the general addition rule is when A and B are two events in a probability experiment. The probability that either one of the events will occur is: P (A or B) = P (A) + P (B) – P (A and B). For example, if you take out a single card from a pack of cards, what is the probability that the card is either an ace or spade? Therefore, P(A) = 4/52, P (B) = 13/52, and P (A and B) = 1/52. P (A or B) = 4/52 + 13/52 – 1/52. P (A or B) = 4/13. Conditional Probability is the probability of one event (A) occurring with a relationship to another event (B). For example, in a sample of 40 vehicles, 18 are red, 6 are trucks, and 2 are both. Suppose that a randomly selected vehicle is red. What is the probability it is a truck? P(truck|red) = P (truck and red) / P (red). P (truck|red) = 2/40 = 18/40 = 2/18 = 1/9 or .11. So, if we must find the probability of an event which will occur given that another event has occurred, we will use conditional probability. If two events are mutually exclusive (no chance of things happening together) and you want to find the probability that an event A or B happens, we will use general addition rule.
"So we could use the general addition rule in the general election (in November elections) and use conditional probability in the primaries?"
In: Statistics and Probability
Python Knapsack Problem:
Acme Super Store is having a contest to give away shopping sprees to lucky families. If a family wins a shopping spree each person in the family can take any items in the store that he or she can carry out, however each person can only take one of each type of item. For example, one family member can take one television, one watch and one toaster, while another family member can take one television, one camera and one pair of shoes.
Each item has a price (in dollars) and a weight (in pounds) and each person in the family has a limit in the total weight they can carry. Two people cannot work together to carry an item. Your job is to help the families select items for each person to carry to maximize the total price of all items the family takes. Write an algorithm to determine the maximum total price of items for each family and the items that each family member should select.
***In python:***
Implement your algorithm by writing a program named “shopping.py”. The program should satisfy the specifications below.
Input: The input file named “shopping.txt” consists of T test cases
T (1 ≤ T ≤ 100) is given on the first line of the input file.
Each test case begins with a line containing a single integer number N that indicates the number of items (1 ≤ N ≤ 100) in that test case
Followed by N lines, each containing two integers: P and W. The first integer (1 ≤ P ≤ 5000) corresponds to the price of object and the second integer (1 ≤ W ≤ 100) corresponds to the weight of object.
The next line contains one integer (1 ≤ F ≤ 30) which is the number of people in that family.
The next F lines contains the maximum weight (1 ≤ M ≤ 200) that can be carried by the ith person in the family (1 ≤ i ≤ F).
Output: Written to a file named “results.txt”. For each test case your program should output the maximum total price of all goods that the family can carry out during their shopping spree and for each the family member, numbered 1 ≤ i ≤ F, list the item numbers 1 ≤ N ≤ 100 that they should select.
Sample Input:
2
3
72 17
44 23
31 24
1
26
6
64 26
85 22
52 4
99 18
39 13
54 9
4
23
20
20
36
Sample Output:
Test Case 1
Total Price 72
Member Items
1: 1
In: Computer Science
The student body of a large university consists of 30% Business majors. A random sample of 6 students is selected.
A. What is the probability that exactly 4 are business majors?
B. What is the probability that no more than 2 are business majors?
C. What is the probability that at least 3 are business majors?
D. What is the probability that less than 5 are business majors?
In: Statistics and Probability
Statistics grades: In a statistics class of 47 students, there were 17 men and 30 women. Three of the men and four of the women received an A in the course. A student is chosen at random from the class. (a) Find the probability that the student is a woman. (b) Find the probability that the student received an A. (c) Find the probability that the student is a woman or received an A. (d) Find the probability that the student did not receive an A.
In: Statistics and Probability
Somebody speculates that a person will test COVID 19 positive with probability 0.2. Then for finding the probability for exactly 100 patients testing positive in a sample of 400 patients, how do you do continuity correction? In the above question, what is the required probability using normal approximation to binomial? What is the probability that at least 70 patients test COVID 19 positive?
In: Statistics and Probability
A normal population has a mean of 57 and a standard deviation of 19. You select a random sample of 19. Use Appendix B.1 for the z-values. Compute the probability that the sample mean is: (Round the final answers to 4 decimal places.)
a. Greater than 60.
Probability
b. Less than 53.
Probability
c. Between 53 and 60.
Probability
In: Statistics and Probability
A normal population has a mean of 64 and a standard deviation of 24. You select a random sample of 32. Use Appendix B.1 for the z-values. Compute the probability that the sample mean is: (Round the final answers to 4 decimal places.)
a. Greater than 67.
Probability
b. Less than 60.
Probability
c. Between 60 and 67.
Probability
In: Statistics and Probability