3 Let X1Xn be a random sample from the distribution wi.pdf

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3. * Let X1,,Xn be a random sample from the distribution with p.d.f. f(x)={e(x),0,x>otherwise where the value of is unknown. (i) * Show that Xn is a biased estimator of . [2 marks] (ii)* Derive an expression for bias (Xn) and discuss what happens to its value as n. [2 marks] (iii)* Can you propose an alternative, unbiased estimator of ?[1mark].

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3. Caesar Cipher (1) You are given a message halloween and a key 4, please encrypt it with Caesar Cipher and show the Ciphertext. Note: We normally use lower case letters to represent plaintext and capital letters to represent ciphertext. (2) Suppose that you have intercepted a message encrypted using Caesar cipher. The ciphertext is OQTPKPI. Please find the key using the brute-force method, and show the plaintext.. Hint: You can convert the letters to the numbers like A>1,B>2,Z>26, then try to subtract each number in the ciphertext by the key value ( k=1,2.).F oreachresult, convert the numbers into letter and check whether it is a meaningful word or sentence..

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3) Bob and Kelly are business partners at the firm of Dewey Cheatham and Howe. They purchased a fishing cabin together on the St. Lawrence river. Each contributed $150,000 . Toward the price of $300,000 After they owned the property for ten years Bob passed away . The cabin was valued at 500,000 on the date of bobs death . What is included in Bob's estate? What if they are father and daughter and Bob makes 3x the money that Kelly makes ?.

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3. A tropical fish fancier produced an albino zebra fish. It lacked blue stripes characteristic of the normal zebra fish. When she crossed a normal zebra fish to the albino, all the offspring were normal. When she crossed two of the normal F1 offspring, X were albino and 1/4 were normal. When an albino was crossed to the normal offspring, half were albino and half were normal. What is the genotype and phenotype of each fish mentioned in this problem? 4. In pea plants, the appearance of flowers along the main stem is a dominant phenotype called "axial" and is controlled by an allele T. The recessive phenotype, produced by an allele t, has flowers only at the end of the stem called "terminal". Pod form displays a dominant phenotype "inflated", controlled by allele F, and a recessive "constricted" form produced by allele f. A pure-breeding axial, constricted plant is crossed to one that is purebreeding terminal, inflated. A. The F1 progeny of this cross are allowed to self-fertilize. What is the expected phenotypic distribution of the F2 progeny? List the genotypes and phenotypes of the F1 generation and the phenotypes of the F2 progeny. B. If an F1 plant from the initial cross described above, is crossed to a plant that is terminal, constricted, what is the expected phenotypic distribution among the resulting progeny?.

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3. (8 pts) Consider the Bayes Net given below. For a given expression of conditional independence, apply D-separation to show the given expression of independence is true or not. Question: Is it guaranteed that F_I_ E | B? Note: Between F and E, there are three paths. Be sure to check ALL three paths and make a conclusion. - Provide the trace of D-separation to show how you arrive at the answer. Answers without the evidence will receive 0 . - A scanned or photo taken image of your work is fine..

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3. (4 pts) Your instructor has presented you with a yery dark gray colored rock (nearly black), and you immediately notice its surface is covered with round holes (a bit like a block of Swiss cheese, except for the dark gray color). It is sparkly, so you know it is made of crystals, but they are much too small for you to recogmize what mineral (or minerals) the rock is made of. It is not noticeably layered, and water just sits on the surface of the rock, and doesn't soak in. Is this rock most likely igneous, sedimentary or metamorphie? What evidence supports your conclusion? What is the significance, if any, of it being made of tiny, almost microscopic crystals? Finally, what is the significance of the round holes?.

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2.Alvin, Simon and Theodore have been in partnership for many years running a vets practice.The partnership agreement states that all drugs are only to be purchased from Dave. Theodore has been suffering from ill health for a number of years and has now retired. Simon has entered into a contract to buy drugs from Brittany. The drugs have been delivered but now Alvin is refusing to pay for them. Dave is also due payment for drugs purchased by the partnership. Task 1:Which TWO of the following statements are correct? A A general partnership begins when the partnership agreement is signed B A general partnership begins when business activity commences C A general partnership must be registered at Companies House D A general partnership does not need to be registered at Companies House (5 marks) Task 2:Which TWO of the following statements are correct? A A partner has only has express authority which is set out in the partnership agreement B A partner has implied authority as set out in Partnership Act 1890 C Simon has acted within his express authority D Simon has acted within his implied authority (5 marks) Task 3:Which TWO of the following statements are correct? A Alvin and Simon are liable for the debts owed to Dave and Brittany B Alvin and Simon are not liable for the debts owed to Dave and Brittany C Theodore is liable for the debts owed to Dave and Brittany D Theodore will not be liable for the debts owed to Dave and Brittany if he has given correct notice of his retirement ( 5 marks).

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2.9) What is the phenotypic distribution for barredeye, wild-type, and intermediate-eye in the F2 generation? Remember to also include information about the sex of the individuals. Identify the homozygous, heterozygous, and hemizygous indivduals. Which phenotypes are observed in the F2 that were not in the parental? 3) Dihybrid cross: The dark-bodied and rudimentary winged genes are on two different autosomal chromosomes. We will use this cross to determine the ratios of phenotypes in the F2 generation when there are two genes involved. 3.1) Use the following symbols to write out the cross: Male: 8 Female: ? Dark body color: DB Wild-type body color: wt Rudimentary wings: Rw Wild-type wings: wtRiw 3.2) What would the cross look like if we mated a Dark-Bodied/Rudimentary winged (double mutant) male with a female that is wild type for both traits? Place the sex of the individual (symbol) on the first set of lines and their respective genotypes in the second set. Sex: Genotypes x 3.3) What are the gametes produced by either sex in the parental generation? Place the symbol for sex on the first set of lines and write down the gametes produced by that sex in the following set of lines, respectively. Sex:3.3) What are the gametes produced by either sex in the parental generation? Place the symbol for sex on the first set of lines and write down the gametes produced by that sex in the following set of lines, respectively. Sex: Gametes produced: 3.4) Using the gametes that you produced from the previous question, fill in the Punnet square and show the resulting offspring from the cross. Place female gametes to the left of the Punnet square and male gametes above. 3.5) What phenotype should the F1 offspring have? 3.6) What would the F1 cross look like if we mated a male F1 and a female F1? Place the sex of the individual on the first set of lines and their respective genotypes in the second set. Sex: Genotypes x 3.7) What are the gametes produced by either sex in the F1 generation? Place the symbol for sex on2.4) Using the gametes that you produced from the previous question, fill in the Punnet square and show the resulting offspring from the cross. Place female gametes to the left of the Punnet square and male gametes above. 2.5) What is the phenotypic distribution for barredeye, wild-type, and intermediate-eye? Remember to also include information about the sex of the individuals. Identify the homozygous, heterozygous, and hemizygous indivduals. Why aren't there any wild-type females? 2.6) What would the F1 cross look like if we mated a male F1 and a female F1? Place the sex (use the symbol) of the individual on the first set of lines and their respective genotypes in the second set (the genotypes should also refect the sex). Sex: Genotypes x 2.7) What are the gametes produced by either sex in the F1 generation? Place the genotypes (these genotypes should display the sex and the trait we are studying) on the first set of lines and write down the gamet.

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