Question: An unfair coin has probability of landing heads. As an experiment, the coin is thrown repeatedly, until the first time it lands tails, after

An unfair coin has probability of landing heads. As an experiment, the

An unfair coin has probability of landing heads. As an experiment, the coin is thrown repeatedly, until the first time it lands tails, after which the experiment ends. Suppose that this full experiment is conducted n times in total, dur- ing which the total number of coin throws is N (this includes all n experiments). (a) Name a probability distribution that is related to the number of throws in a single experiment. (2 marks) (b) Explain in words why we can expect that, on average, 3N/5 = n. (8 marks) (c) Use part (b) to explain why the expected number of throws in a single experiment is 5/3. (5 marks) (d) Now suppose that the experiment is modified so that it stops only after 500 coins have landed tails, and before each throw, the thrown coin is selected randomly between two coins (each with probability 0.5) : one coin has probability of landing heads and the other coin has probability of landing heads. By modifying the arguments you used in (b) and (c), or other- wise, find the expected total number of throws for the full modi- fied experiment to be performed 6 times in a row. (10 marks)

Step by Step Solution

★★★★★

3.49 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Lets address each part of the question step by step a Name a probability distribution that is related to the number of throws in a single experiment The experiment in question involves throwing a coin ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

(a) Prove by the Principle of Mathematical Induction that n > (2i 1) = n? i=1 (7 Marks) (b) Prove by contradiction that there are infinitely many prime numbers. (7 Marks) (c) Knowing that sequence...

In Imaginationland, each person has exactly one child. Suppose that a child of a pro video gamer is also a pro video gamer with prob- ability 0.7, or an amateur video gamer with probability 0.3....

Suppose that the joint density function for two continuous random variables X and Y is defined by fxx(r,y) = cry', if 0

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

An unfair coin has probability 2/5 of landing heads. As an experiment, the coin is thrown repeatedly, until the first time it lands tails, after which the experiment ends. Suppose that this full...

1. The choices for problem number 10, from section 6.5, in the book are given below. a. 0.4054 b. 0.1500 c. 0.5946 d. 0.7321 e. 0.2381 2. The choices for problem number 38 part d, from section 6.5,...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Algorithms in Artificial Intelligence (or, the old name: Introduction to Algorithmic Decision Making) Part 1 Based on slides by David Sarne and Lirong Xia Course Tentative Schedule Introduction...

Help me answer all of the following activities, follow the pages for easy format thank you Activity 1. Find Me! Directions: Find the probability of the following events. 1. Getting an even number in...

A discrete sequence {xn} can be converted into a continuous representation x(t) = ts X n= (t n ts) xn, where ts is the sampling period. (a) State two characteristic properties of Dirac's function. [2...

ABC Company is considering two alternative investment projects. The following information is provided: Project A: Initial investment: $100,000 Annual net cash inflows for 4 years: $35,000 Project B:...

Give the phase and the specific volume. Discuss in detail.

When Pepsi introduced Pepsi Zero, they were injing to mensure how mony corsumers would choose Pepal Zero over Coke Zere if given the option. What brand metric were they trying to messure? Brand...

The following data pertain to British Isles Aggregates Company, a producer of sand, gravel, and cement, for the year just ended. Sales revenue ......... 2,000,000 Cost of goods sold ............

SilverEdge Systems Software hired Catherine Conrad to perform a singing telegram. SilverEdge arranged for James Bendewald to record Conrads performance of her copyrighted song to post on its Web...

Refer to the preceding exercise. Income ............. $ 4,000,000 Sates revenue ........... 50,000,000 Average invested capital ...... 20,000,000 Required: Demonstrate two ways Dakota Divisions...

The following data pertain to Dakota Divisions most recent year of operations. Income ............. $ 4,000,000 Sates revenue ........... 50,000,000 Average invested capital ...... 20,000,000...

John and Andrew Doney invented a hard-bearing device for balancing rotors. Although they obtained a patent for their invention from the U.S. Patent and Trademark Office, it was never used as an...

When a nonprice determinant of supply changes what will be the effect on the market? Multiple choice question. A shift in the supply curve at all possible prices A shift in the supply curve above the...

A researcher wishes to estimate the mean amount of money spent per month on food by households in a certain neighborhood. She desires a margin of error of $30. Past studies suggest that a population...

Flawed parts: On a certain day, a foundry manufactured 015 cast aluminum parts, Some of these had major flaws, some had minor flaws, and some had both major and minor flaws, The following table...

An unfair coin has probability 0

I feel like I am missing a step. I am unsure where how this equation arrived at 0.6. An unfair coin has probability 0.4 of landing heads. The ooin is tossed four times. What is the probability that...

Problem 1: Flipping an unfair coin, the probability of a head is 0.6. 1. What is the probability of a tail? 2. We toss this coin three times. Let X be the number of heads. What is the probability...

A ALEKS - Maker X LU BIOL 103: Principl Lu Lab Activity: Two LU BIOL 101: Princip! Biomolecules of Cells Cengage Digital ! MLA Citation Ger X Grades for Maker Biological Macromol...