1. Suppose that we toss a fair coin three times and record the outcomes observed inthe first, second, and third toss respectively.a) List the possible events of this experiment.b) Determine the sample space of the experiment and present it using set notation.c) Show the σ-algebra I and find the number of subsets.d) What does the result in (c) indicate to you?

a) List the possible events of this experiment:For each toss of the fair coin, there are two…

Answered: 1. Suppose that we toss a fair coin…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a sample space S. Let A and B be any two events in S. Write the expressions in terms of unions, interactions, and complements for the following events
Consider the following experiment. A coin is tossed three times and the upper face (head or tail) is recorded for each toss. Use a tree diagram to find the simple events for the experiment. (Enter your answers as a comma-separated list. Enter each simple event in the format (O1, O2, O3) where Oi is the outcome of the ith toss. Use H for heads and T for tails.)
13. Heather is interested in determining the probability that a randomly selected card from a standard deck of 52 will be a club. She reasons that the deck contains clubs (C), spades (S) diamonds (D), and hearts (H). She constructs the sample space S = (C,S,D,H). Determine if the sample points are equally likely or not equally likely.
(a) A bank analyst wants to ask customers who have a mortgage with the bank about the customers' home-buying experiences. Which of the following best describes a random sample of customers? The analyst forms groups of 9 customers based on the cities the customers live in. Then, she selects all of the customers in 6 randomly chosen groups. The analyst spends a day calling mortgage customers and selects the first 54 customers who answer because these customers are easily accessible. The analyst uses a computer program to draw 54 customers at random and selects these customers. Every set of 54 customers is equally likely to be drawn by the computer program. (b) A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a stratified sample of seats? The supervisor uses a computer program to draw 60 seats at random and selects these seats. Every set of 60 seats is equally likely to be drawn by the computer…
a as a list b as a table c as a tree diagram 4 Four cards marked 6, 7, 8 and 9 are in a hat. One card is drawn out and placed on a table. This is to be the tens digit of a two-digit number. Another card is then drawn out of the hat and placed beside the first card to complete the number. a Draw a tree diagram to show the sample space of this experiment. b How many outcomes are in the sample space? c If the cards are drawn at random, what is the chance of getting the number 78?
Naive Approach 1: Say A, B, C are independent ifP (A ∩B ∩C) = P (A)P (B)P (C).Suppose two six-sided dice are tossed and the outcome is noted. Let S denotethe sample space of this experiment.i. Write down the set S explicitly. Consider the eventsA = {(i, i) : i = 1, 2, 3, 4, 5, 6}, B = {(x, y) : 7 ≤x + y ≤10},C = {(x, y) : x + y is 2 or 7 or 8}.Write down the sets A, B, and C explicitly and calculate P (A), P (B), andP (C).
1. You roll a pair of standard dice. The sample space is as follows: 田围图图图图国圈国目图图图围 A. P (getting a 1 on the first die or getting a 5 on the second die) B. P (sum of the dice = 8) c. P (getting a 3 on the second die given that you got a 2 on the first die) D. P (getting an odd number on the first die and a value greater than 4 on the second die) E. P (getting a value greater than 4 on the first die given a sum of 8)
Homecoming. A college Statistics class conducted a survey concerning community attitudes about the col-lege’s large homecoming celebration. That survey drew its sample in the following manner: Telephone numberswere generated at random by selecting one of the localtelephone exchanges (first three digits) at random andthen generating a random four-digit number to followthe exchange. If a person answered the phone and thecall was to a residence, then that person was taken to bethe subject for interview. (Undergraduate students andthose under voting age were excluded, as was anyonewho could not speak English.) Calls were placed until asample of 200 eligible respondents had been reached.a) Did every telephone number that could occur in thatcommunity have an equal chance of being generated?b) Did this method of generating telephone numbersresult in a simple random sample (SRS) of localresidences? Explain.c) Did this method generate an SRS of local voters?Explain.d) Is this method unbiased in…

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