Tossing an unfair coin with P(H) = 0.6 and P(T) = 0.4. The coin is tossed...
Tossing an unfair coin with P(H) = 0.6 and P(T) = 0.4. The coin is tossed 10 times (each toss is independent from others) and in any turn it shows heads, it is tossed again. We want to count the cases where the coin is tossed twice and the second toss, too, is head.
For example,
H T T T T T T T H T
H T
In this case, the count will be 1. Only the first turn is counted.
Let X be the counted number of such double heads. What is the support, pmf, expected value and variance of X?
Homework Answers
Add Answer to:
Tossing an unfair coin with P(H) = 0.6 and P(T) = 0.4. The coin
is tossed...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes...
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
An unfair coin has probability 0.4 of landing heads. The coin is tossed seven times. What...
An unfair coin has probability 0.4 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round your answer to four decimal places. P (Lands heads at least once) -
One application of an absolute value inequality is the concept of the unfair coin. If a coin is tossed 100 times, w...
One application of an absolute value inequality is the concept of the unfair coin. If a coin is tossed 100 times, we would expect approximately 50 of the tosses to be heads; however this is rarely the case.1. Toss a coin 100 times to test this hypothesis. Record the number of times the coin is heads and the number of times the coin is tails on the lines below. You may want to ask someone to tally the results of...
E. A coin with probabiltiy p of heads is tossed till the first head occurs. It...
E. A coin with probabiltiy p of heads is tossed till the first head occurs. It 1S is then tossed again till the first tail occurs. Let X be the total number of tosses required (a) Find the PMF of X, (b) Find the mean and variance of X
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of...
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are...
An experiment consists of tossing an unfair coin (53% chance of landing on heads) a specified...
An experiment consists of tossing an unfair coin (53% chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.) Does this probability change if we toss the coin three times? What if we toss the coin four times? The probability changes if we toss the coin three times, but does not change if we toss the coin...
An experiment consists of tossing an unfair coin (49% chance of landing on heads) a specified...
An experiment consists of tossing an unfair coin (49% chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.) Does this probability change if we toss the coin three times? What if we toss the coin four times? The probability changes if we toss the coin four times, but does not change if we toss the coin...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4. If we let X be the number of coin tosses that come up heads, observe that the possible values of Xare 0, 1, 2, and 3. Find the probability distribution of X. Hint: the problem can be solved...
A coin will be tossed twice, and each toss will be recorded as heads ( H...
A coin will be tossed twice, and each toss will be recorded as heads ( H ) or tails ( T ). Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the first toss is heads. Use the format HT to mean that the first toss is heads and the second is tails. If there is more than one element in the set, separate them with commas. Samplespace: Eventthatthefirsttossisheads:
A coin will be tossed twice, and each toss will be recorded asheads (H...
A coin will be tossed twice, and each toss will be recorded as heads (H) or tails (T).Give the sample space describing all possible outcomes.Then give all of the outcomes for the event that the second toss is tails.Use the formatHTto mean that the first toss is heads and the second is tails.If there is more than one element in the set, separate them with commas.
2. Consider tossing a coin twice. Denote H ="head" and T ="tail" (a) List all outcomes in the sample space S (b) Let X count the number of heads. List all outcomes in the events Ao = {X = 0}, Ai = {X=1 and A2 {X = 2}. Are all the events Ao,A1,A2 mutually exclusive? Explain. (c) Suppose P(H) = 0.6. Find the probability mass function of X: f(x) = P{X =x} (d) Find the cumulative distribution function of X:...
An unfair coin has probability 0.4 of landing heads. The coin is tossed seven times. What is the probability that it lands heads at least once? Round your answer to four decimal places. P (Lands heads at least once) -
E. A coin with probabiltiy p of heads is tossed till the first head occurs. It 1S is then tossed again till the first tail occurs. Let X be the total number of tosses required (a) Find the PMF of X, (b) Find the mean and variance of X
Problem(13) (10 points) An unfair coin is tossed, and it is assumed that the chance of getting a head, H. is (Thus the chance of setting tail, T. is.) Consider a random experiment of throwing the coin 5 times. Let S denote the sample space (a) (2 point) Describe the elements in S. (b) (2 point) Let X be the random variable that corresponds to the number of the heads coming up in the four times of tons. What are...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4. If we let X be the number of coin tosses that come up heads, observe that the possible values of Xare 0, 1, 2, and 3. Find the probability distribution of X. Hint: the problem can be solved...
Most questions answered within 3 hours.
-
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 1 hour ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 1 hour ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 3 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 3 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 3 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 3 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 3 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 3 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 3 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 3 hours ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 3 hours ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 3 hours ago