2. John has a special coin and he claims that it lands head 67% of the...

2. John has a special coin and he claims that it lands head 67% of the time it is tossed.

a. What is the probability that in 22 tosses, the coin would land heads 13 or fewer times?

b. If John actually tossed the coin 22 times and obtained 13 heads, would you have a good reason to doubt that John’s claim (head lands head 67% of the time) is true? Explain your answer.

Expert Solution

thank you.

orchestra answered 2 years ago

A player tosses a fair coin n times. Each time, if the coin lands on Head,...

A player tosses a fair coin n times. Each time, if the coin lands on Head, the player win a dollar, otherwise, the player loses a dollar. What is the expected earning of the player? What is the variance of the earning of the player? Now the player apply a new strategy: the player will play the game until he gets a head. What is the expected earning of the new strategy? Does the result depend on n?

Peter and John are tossing a coin. If it is a Head, then peter will give...

Peter and John are tossing a coin. If it is a Head, then peter will give John 1dollar. If it is a Tail, then John will give Peter 1dollar. Suppose Peter has a dollar, John has b dollar. Question: the probability that Peter wins all the money from John.

- Your friend claims he has a fair coin; that is, the probability of flipping heads...

- Your friend claims he has a fair coin; that is, the probability of flipping heads or tails is equal to 0.5. You believe the coin is weighted. Suppose a coin toss turns up 15 heads out of 20 trials. At α = 0.05, can we conclude that the coin is fair (i.e., the probability of flipping heads is 0.5)? You may use the traditional method or P-value method.

Is this coin balanced? While he was a prisoner of war during world war 2, John...

Is this coin balanced? While he was a prisoner of war during world war 2, John Kerrich tossed a coin 10,000 times. He counted how many times he got heads. a. Is this setting binomial? Explain using the four characteristics of a binomial setting. b. He got 5067 heads. if the coin is perfectly balanced, the probability of a head is 0.5. Is there reason to think that Kerrich’s coin was not balanced? To answer this question, find the probability...

10.2) John has two unfair coins, and he claims that they are from the same model...

10.2) John has two unfair coins, and he claims that they are from the same model with the probability of obtaining a head being 0.4. Coin A is tossed 100 times and 38 heads are observed. Coin B is tossed 200 times and 86 heads are observed. At the significance level α being 0.05, check whether these two coins are identical

Take a coin that lands “heads” with probability 1/2 and flip it repeatedly while keeping trackof...

Take a coin that lands “heads” with probability 1/2 and flip it repeatedly while keeping trackof the pattern of “heads” and “tails” that you see. Use 1 to denote a “head” and 0 to denotea “tail”. We are interested in computing the frequency of the pattern{1, 1, 0}, i.e., of seeingtwo consecutive “heads” followed by a “tail”. To do this we construct a Markov chain whosestate space consists of all the possible 3-flip patterns:1){1, 1, 1}2){1, 1, 0}3){1, 0, 1}4){0,...

Each day John performs the following experiment. He flips a fair coin repeatedly until he sees...

Each day John performs the following experiment. He flips a fair coin repeatedly until he sees a T and counts the number of coin flips needed. (a) Approximate the probability that in a year there are at least 3 days when he needed more than 10 coin flips. Argue why this approximation is appropriate. (b) Approximate the probability that in a year there are more than 50 days when he needed exactly 3 coin flips. Argue why this approximation is...

Suppose you flip a biased coin (that lands heads with probability p) until 2 heads appear....

Suppose you flip a biased coin (that lands heads with probability p) until 2 heads appear. Let X be the number of flips needed for this two happen. Let Y be the number of flips needed for the first head to appear. Find a general expression for the condition probability mass function pY |X(i|n) when n ≥ 2. Interpret your answer, i.e., if the number of flips required for 2 heads to appear is n, what can you say about...

1 An individual is holding an ancient coin and claims that he got money. Discuss whether...

1 An individual is holding an ancient coin and claims that he got money. Discuss whether his claim is true or false? State your justification.? 2 What do you mean by money has “intrinsic value”? 3 An individual has Centurion® Card from American Express (credit cards). The credit card is most valuable credit card in the world. Can this individual claim that he/she is a wealthy individual? 4 Why do we need a Central Bank for an economy?

An individual is holding an ancient coin and claims that he got money. Discuss whether his...

An individual is holding an ancient coin and claims that he got money. Discuss whether his claim is true or false? State your justification. What do you mean by money has “intrinsic value”? An individual has Centurion® Card from American Express (credit cards). The credit card is most valuable credit card in the world. Can this individual claim that he/she is a wealthy individual?

Question