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Lel X_1,...X_n be independent and identically distributed continuous random variables having cumulative distribution function F(x) and and density function f(x). The quantity M = [X_11 + X_11]/2. defined to be the average of the smallest and largest values in X_1...X_11 is called the \"midrange\" of the sequence. Show that M has the cumulative distribution function Also calculate this function when X, are (a) independent identical Exponential random variables with parameter lambda. and (b) independent identical Uniform (O.I) random variables. Solution a) as you can see FM(M) has a f(x) multiply by the distribution of F since we know that f(x) is a probability distribution (mass) we knwo that if we multiply that for Fm we willhave a cumulative distribution function.

Lel X_1,...X_n be independent and identically distributed continuous random variables having
cumulative distribution function F(x) and and density function f(x). The quantity M = [X_11 +
X_11]/2. defined to be the average of the smallest and largest values in X_1...X_11 is called the
"midrange" of the sequence. Show that M has the cumulative distribution function Also
calculate this function when X, are (a) independent identical Exponential random variables with
parameter lambda. and (b) independent identical Uniform (O.I) random variables.
Solution
a)
as you can see FM(M) has a f(x) multiply by the distribution of F
since we know that f(x) is a probability distribution (mass) we knwo that if we
multiply that for Fm we willhave a cumulative distribution function

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Amino acids are joined together to make proteins in what kind of reactions? Hydrolysis hydration synthesis catabolic dehydration synthesis Solution Answer: 44. (d) Dehydration synthesis A peptide bond is a chemical bond formed between two molecules when the carboxyl group of one molecule reacts with the amino group of the other molecule, releasing a molecule of water (H2O). This is a dehydration synthesis reaction (also known as a condensation reaction), and usually occurs between amino acids resulting in the formation of a polypeptide chain..

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7. Mendel\'s Principle of Segregation states that the alleles of a gene will separate from one another during the formation of gametes. Consider the genotype Aa. If crossing-over does not occur, when specifically will these alleles separate? a. Mitosis or Meiosis I b. Mitosis and Meiosis II c. Meiosis I or Meiosis II d. Meiosis I e. Meiosis II 8. A student is studying 5 unlinked genes (referred to simply as gene 1, gene 2, gene 3, gene 4 and gene 5. The alleles of gene 1 are represented as A and a; the alleles for gene 2 are represented with the letters B and b; the alleles of gene 3 are Cand c, and so on. An individual has the genotype Aa Bb Cc Dd Ee. How many allele combinations can be made with the genotype? 2 a. b. 5 c. 10 d. 20 e. 32 Solution 7. (e) The alleles separate in the second part of meiosis, and form hapliod gametes. 8. (e) 32, Here n=5 so 2^5=32 1. (b) There are two non homologous chromosomes present. Each set of chromosome has one chromosome from each parent..

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4. Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? What are the hypothesis statements: Ho: Ha: Do manual calculations per cell here (if desired) A B C D E F A B C D E F OBS COUNT - m M OBS COUNT - f F Sum = EXPECTED What is the value of the chi square statistic: What is the p-value associated with this value: Is the p-value <0.05? Do you reject or not reject the null hypothesis: If you rejected the null, what is the Phi correlation: What does this correlation mean? What does this decision mean for our equal pay question: ID Salary Compa Midpoint Age Performance Rating Service Gender Raise Degree Gender1 Gr 1 66.1 1.159 57 34 85 8 0 5.7 0 M E 2 25.9 0.834 31 52 80 7 0 3.9 0 M B 3 35.2 1.135 31 30 75 5 1 3.6 1 F B 4 55.3 0.971 57 42 100 16 0 5.5 1 M E 5 49.6 1.033 48 36 90 16 0 5.7 1 M D 6 78.3 1.168 67 36 70 12 0 4.5 1 M F 7 42.3 1.058 40 32 100 8 1 5.7 1 F C 8 22.8 0.990 23 32 90 9 1 5.8 1 F A 9 78 1.164 67 49 100 10 0 4 1 M F 10 23.3 1.014 23 30 80 7 1 4.7 1 F A 11 23.6 1.025 23 41 100 19 1 4.8 1 F A 12 60.8 1.067 57 52 95 22 0 4.5 0 M E 13 40.6 1.014 40 30 100 2 1 4.7 0 F C 14 21.7 0.943 23 32 90 12 1 6 1 F A 15 21.8 0.949 23 32 80 8 1 4.9 1 F A 16 37.4 0.934 40 44 90 4 0 5.7 0 M C 17 57 1.000 57 27 55 3 1 3 1 F E 18 33.5 1.081 31 31 80 11 1 5.6 0 F B 19 23 1.000 23 32 85 1 0 4.6 1 M A 20 36 1.162 31 44 70 16 1 4.8 0 F B 21 76 1.135 67 43 95 13 0 6.3 1 M F 22 43.7 0.911 48 48 65 6 1 3.8 1 F D 23 25.3 1.098 23 36 65 6 1 3.3 0 F A 24 48.9 1.019 48 30 75 9 1 3.8 0 F D 25 25.8 1.122 23 41 70 4 0 4 0 M A 26 23.3 1.013 23 22 95 2 1 6.2 0 F A 27 42.3 1.057 40 35 80 7 0 3.9 1 M C 28 75.2 1.122 67 44 95 9 1 4.4 0 F F 29 80.9 1.208 67 52 95 5 0 5.4 0 M F 30 49 1.020 48 45 90 18 0 4.3 0 M D 31 24.2 1.054 23 29 60 4 1 3.9 1 F A 32 27.5 0.886 31 25 95 4 0 5.6 0 M B 33 63.6 1.115 57 35 90 9 0 5.5 1 M E 34 28.6 0.922 31 26 80 2 0 4.9 1 M B 35 22.4 0.976 23 23 90 4 1 5.3 0 F A 36 23.6 1.026 23 27 75 3 1 4.3 0 F A 37 24.3 1.057 23 22 95 2 1 6.2 0 F A 38 63 1.105 57 45 95 11 0 4.5 0 M E 39 34.8 1.123 31 27 90 6 1 5.5 0 F B 40 24.3 1.057 23 24 90 2 0 6.3 0 M A 41 42.8 1.071 40 25 80 5 0 4.3 0 M C 42 23 0.998 23 32 100 8 1 5.7 1 F A 43 75.4 1.125 67 42 95 20 1 5.5 0 F F 44 60.7 1.065 57 45 90 16 0 5.2 1 M E 45 57.9 1.206 48 36 95 8 1 5.2 1 F D 46 62.2 1.091 57 39 75 20 0 3.9 1 M E 47 62.2 1.091 57 37 95 5 0 5.5 1 M E 48 70.1 1.230 57 34 90 11 1 5.3 1 F E 49 61.7 1.083 57 41 95 21 0 6.6 0 M E 50 61.4 1.077 57 38 80 12 0 4.6 0 M E A B C D E F A B C D E F OBS COUNT - m M OBS COUNT - f F Sum = EXPECTED Solution Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? What are the hypothesis statements: Ho: Males and females are distributed across grades in a similar pattern within the population Ha: Males and females are distributed across grades in a different pattern within the population Obs.

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An unassuming single-celled organism called Toxoplasma gondii is one of the most successful parasites on Earth, infecting an estimated 11 percent of Americans and perhaps half of all people worldwide. It’s just as prevalent in many other species of mammals and birds. In a recent study in Ohio, scientists found the parasite in three-quarters of the white-tailed deer they studied. One reason for Toxoplasma’s success is its ability to manipulate its hosts. The parasite can influence their behavior, so much so that hosts can put themselves at risk of death. Scientists first discovered this strange mind control in the 1990s, but it’s been hard to figure out how they manage it. Now a new study suggests that Toxoplasma can turn its host’s genes on and off — and it’s possible other parasites use this strategy, too. Toxoplasma manipulates its hosts to complete its life cycle. Although it can infect any mammal or bird, it can reproduce only inside of a cat. The parasites produce cysts that get passed out of the cat with its feces; once in the soil, the cysts infect new hosts. Toxoplasma returns to cats via their prey. But a host like a rat has evolved to avoid cats as much as possible, taking evasive action from the very moment it smells feline odor. Experiments on rats and mice have shown that Toxoplasma alters their response to cat smells. Many infected rodents lose their natural fear of the scent. Some even seem to be attracted to it. Manipulating the behavior of a host is a fairly common strategy among parasites, but it’s hard to fathom how they manage it. A rat’s response to cat odor, for example, emerges from complex networks of neurons that detect an odor, figure out its source and decide on the right response in a given moment. Within each of the neurons in those networks, thousands of genes are producing proteins and other molecules essential for relaying all of the necessary information throughout the body. Simple Toxoplasma seems ill-equipped to take over such a complicated system. But a new study published in the journal Molecular Ecology hints that the parasite can do so by relying on an eerily elegant strategy. Think of the genes in a host as keys on a piano. Toxoplasma, it seems, simply plays some of the keys differently to produce a new melody. A rat is made up of lots of different kinds of cells, from the neurons in its brain to the bone-producing cells in its skeleton to the insulin-making cells in its pancreas. Yet all of them carry the same 20,000 genes. Depending on the function of a particular cell, some of its genes are switched on and others are shut down. Genes may be switched off, or silenced, by the attachment of molecular caps called methyl groups, a process called methylation. In order to switch a gene on again, the caps are removed. Methylation does more than just allow cells to develop into a variety of organs. It lets them change the way they work in response to signals from the outside. In the brain, for example, neuron.

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A diploid organism has a somatic chromosome number of 16. The centromeres of the 8 homologouspairs are designated as Aa, Bb, Cc, Dd, Ee, Ff, Gg and Hh, with uppercase letters referring to the centromeres of maternal chromosomes and lowercase letters to the centromeres of paternal chromosomes. Each centromere represents one chromosome. Where n = the haploid chromosome number. How many different combinations of centromeres could be produced during meiosis? a.) 8 b.) 64 c.) 256 d.) 512 e.) 6561 Solution At the meiosis, total number of chromosome is 16. During the meiosis 1st spliting of homologous chromosome take place, so each cell has 8 chromosome and centromere..

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the heights of a sample of 10 father/son pairs of subjects were measured. Minitab results are shown below. Is there sufficient evidence to support the claim that there is a linear correlation between the heights of fathers and the heights of their sons? explain (use significance level of 0.05) Pearson correlation of FATHER and SON= 0.149 P-value=0.681 How do I begin to answer this problem? How do I use the values they give me to get the answer? Solution.

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Should the FCC regulate the media, and if yes, how far should you go? Should it require toning down sex and violence, airing the shows only later at night, or should it take down shows like Sex and the City off air? Solution The FCC also acts as a police agency of the airwaves, and it can fine broadcasters for violating public decency standards on the air. Critics contend that media consolidation limits consumers’ choices because a small number of companies own all the media outlets. They argue that consolidation is not competitive and that corporate owners might restrict or manipulate news coverage. Some critics also lament the homogenization of American culture due to media consolidation. Because radio and television formats have become increasingly uniform, people throughout the country receive the same broadcasts..

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