Homework Answers
In general case when Heads will be the outcome we will stop the experiment. And in second case it is possible that Heads will come in first toss or it can be in second toss when first toss in tails, third toss when first two outcomes are tails.
Add Answer to:
1. Consider the experi We toss a coin until we obtain a head Wrie down the...
2. We take a rod of length 1 metre and randomly divide it into two pieces....
2. We take a rod of length 1 metre and randomly divide it into two pieces. Write down the sample space for this experiment. Can you plot it? Write down the event E that at least one of the pieces has length strictly bigger than 1/2 metre. 3. How many ways are there to color n different balls with 4 colors?
9.74. Suppose we toss a biased coin independently until we get two heads or two tails...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
A5 Consider an experiment where you toss a coin as often as necessary to turn up...
A5 Consider an experiment where you toss a coin as often as necessary to turn up one head. Suppose that the probability of having a tail is p (obviously probability of a head is 1 - p). Assume independence between tosses. a) State the sample space. b) Let X be the number of tosses needed to get one head. What is the support (possible values of X)? c) Find P(X = 1), P(X = 2) and P(X = 3). d)...
Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3....
Suppose you toss an unfair coin 8 times independently. The probability ofgetting a head is 0.3. Denote the outcome to be 1 if you get a head and 0 if a tail. (i) Write down the sample space Ω. (ii) What is the probability of the event that you get a head or a tail at least once? (iii) If you get eight same toss's you will get x dollars, otherwise you will lose 1 dollar. On average, how large...
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of hea...
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved?
Suppose...
Example 5.5. We roll a fair die then toss a coin the number of times shown...
Example 5.5. We roll a fair die then toss a coin the number of times shown on the die. What is the probability of the event A that all coin tosses result in heads? One could use the state space Ω = {(1, H), (1, T), (2, H, H), (2, T, T), (2, T, H), (2, H, T), . . . }. However, the outcomes are then not all equally likely. Instead, we continue the state space is Ω {1,...
Suppose we toss a fair coin every second so the first toss is at time t1. Define a random variabl...
Suppose we toss a fair coin every second so the first toss is at time t1. Define a random variable Y (the "waiting time for the first head ") by Prove that Yi satisfies (Yİ is said to have geometric distribution with parameter p. (Yi-n) = (the first head occurs on the n-th toss). FOUR STEPS TO THE SOLUTION (1) Express the event Yǐ > n in terms of , where , is the number of heads after n tosses...
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head,...
Imagine an experiment where we flip a coin 6 times, and get “head, tail, head, head, head, head”. Which of the following statements are true? a) The coin is not fair b) The coin’s tail probability is 1/6 c) The sequence "head, tail, head, head, head, head" is an outcome in the sample space. d) The sample space of the experiment is {head, tail}
1. (a) What is the sample space S for flipping a coin until you get a...
1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements. (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on the green die...
Problem 6 7. Part 1-4 (10pts)A coin has two faces Head and Tail. (1) (2pts)]lf you...
Problem 6
7. Part 1-4
(10pts)A coin has two faces Head and Tail. (1) (2pts)]lf you toss the coin once, and record the up-face value, what is the sample space? 6. (2) (2pts)lf you toss the coin once, what is the probability that up-face is Tail? What is the probability that up-face is Head? (3) (5ps)lf you toss the coin three times, and record the up-face value for each toss. One of the possible outcome is (Head, Head, Head). By...
2. We take a rod of length 1 metre and randomly divide it into two pieces. Write down the sample space for this experiment. Can you plot it? Write down the event E that at least one of the pieces has length strictly bigger than 1/2 metre. 3. How many ways are there to color n different balls with 4 colors?
A5 Consider an experiment where you toss a coin as often as necessary to turn up one head. Suppose that the probability of having a tail is p (obviously probability of a head is 1 - p). Assume independence between tosses. a) State the sample space. b) Let X be the number of tosses needed to get one head. What is the support (possible values of X)? c) Find P(X = 1), P(X = 2) and P(X = 3). d)...
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved?
Suppose...
Example 5.5. We roll a fair die then toss a coin the number of times shown on the die. What is the probability of the event A that all coin tosses result in heads? One could use the state space Ω = {(1, H), (1, T), (2, H, H), (2, T, T), (2, T, H), (2, H, T), . . . }. However, the outcomes are then not all equally likely. Instead, we continue the state space is Ω {1,...
Suppose we toss a fair coin every second so the first toss is at time t1. Define a random variable Y (the "waiting time for the first head ") by Prove that Yi satisfies (Yİ is said to have geometric distribution with parameter p. (Yi-n) = (the first head occurs on the n-th toss). FOUR STEPS TO THE SOLUTION (1) Express the event Yǐ > n in terms of , where , is the number of heads after n tosses...
1. (a) What is the sample space S for flipping a coin until you get a head or 4 consecutive tails? Write down your sample space by listing the elements. (b) An experiment involves tossing a pair of dice, one green and one red, recording the numbers that come up. These are special dice. Each die has only 5 sides and are labeled with the numbers 1, 2, 3, 4, 5. Let r be the outcome on the green die...
Problem 6
7. Part 1-4
(10pts)A coin has two faces Head and Tail. (1) (2pts)]lf you toss the coin once, and record the up-face value, what is the sample space? 6. (2) (2pts)lf you toss the coin once, what is the probability that up-face is Tail? What is the probability that up-face is Head? (3) (5ps)lf you toss the coin three times, and record the up-face value for each toss. One of the possible outcome is (Head, Head, Head). By...
Most questions answered within 3 hours.
-
The free energy change for the following reaction at 25 °C, when
[Sn2+] = 1.17 M...
asked 42 minutes ago -
An MNE is this kind of industry when competition in one country
is essentially independent of...
asked 2 hours ago -
. For this set of questions, determine what
proportion of a normal distribution is located betweeneach...
asked 2 hours ago -
A college student is employed as a door-to-door newspaper
salesman. Historical data suggests that the student...
asked 3 hours ago -
MATLAB HW 11 problem using Switch Case and Input commands
Write a script file that calculates...
asked 3 hours ago -
Considering gravitational time dilation, calculate the time that
passes in Earth’s surface while 1 hour passes...
asked 4 hours ago -
Minitab Problem: Take the Lake Hume June rainfall data and find
use the processes outlined in...
asked 5 hours ago -
X Company is trying to decide whether to continue using old
equipment to make Product A...
asked 5 hours ago -
IN PYTHON ONLY !! Program 2: Re-work
program #5 (WeeklyHours) from the previous assignment such that...
asked 5 hours ago -
The average length of time between arrivals at a turnpike
toll-booth is 26 seconds. What is...
asked 7 hours ago -
(a) A piston at 6.1 atm contains a gas that occupies a volume of
3.5 L....
asked 8 hours ago -
Please answer true or false. Words
cannot be changed or added in to make it true...
asked 8 hours ago