Binomial Table for n=2, n=3, n=4, n=5 and n=6

One important discrete random variable is a binomial random variable. The distribution of this type of variable, referred to as the binomial distribution, is completely determined by two parameters: n   and p.   Here n is the number of trials and p is the probability of success. The tables below are for n 2, 3, 4, 5 and 6. The probabilities in each are rounded to three decimal places. Before using the table, it is important to determine if a binomial distribution should be used. In order to use this type of distribution, we must make sure that the following conditions are met: We have a finite number of observations or trials.The outcome of teach trial can be classified as either a success or a failure.The probability of success remains constant.The observations are independent of one another. The binomial distribution gives the probability of r successes in an experiment with a total of n independent trials, each having probability of success p.  Ã‚   Probabilities are calculated by the formula C(n, r)pr(1 - p)n - r where C(n, r) is the formula for combinations. Each entry in the table is arranged by the values of p and of r.   There is a different table for each value of n.   Other Tables For other binomial distribution tables: n 7 to 9, n 10 to 11.   For situations in which np  and n(1 - p) are greater than or equal to 10, we can use the normal approximation to the binomial distribution.   In this case, the approximation is very good and does not require the calculation of binomial coefficients.   This provides a great advantage because these binomial calculations can be quite involved. Example To see how to use the table, we will consider the following example from genetics.   Suppose that we are interested in studying the offspring of two parents who we know both have a recessive and dominant gene.   The probability that an offspring will inherit two copies of the recessive gene (and hence have the recessive trait) is 1/4.   Suppose we want to consider the probability that a certain number of children in a six-member family possesses this trait.   Let X be the number of children with this trait.   We look at the table for n 6 and the column with p 0.25, and see the following: 0.178, 0.356, 0.297, 0.132, 0.033, 0.004, 0.000 This means for our example that P(X 0) 17.8%, which is the probability that none of the children has the recessive trait.P(X 1) 35.6%, which is the probability that one of the children has the recessive trait.P(X 2) 29.7%, which is the probability that two of the children have the recessive trait.P(X 3) 13.2%, which is the probability that three of the children have the recessive trait.P(X 4) 3.3%, which is the probability that four of the children have the recessive trait.P(X 5) 0.4%, which is the probability that five of the children have the recessive trait. Tables for n2 to n6 n 2 p .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 r 0 .980 .902 .810 .723 .640 .563 .490 .423 .360 .303 .250 .203 .160 .123 .090 .063 .040 .023 .010 .002 1 .020 .095 .180 .255 .320 .375 .420 .455 .480 .495 .500 .495 .480 .455 .420 .375 .320 .255 .180 .095 2 .000 .002 .010 .023 .040 .063 .090 .123 .160 .203 .250 .303 .360 .423 .490 .563 .640 .723 .810 .902 n 3 p .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 r 0 .970 .857 .729 .614 .512 .422 .343 .275 .216 .166 .125 .091 .064 .043 .027 .016 .008 .003 .001 .000 1 .029 .135 .243 .325 .384 .422 .441 .444 .432 .408 .375 .334 .288 .239 .189 .141 .096 .057 .027 .007 2 .000 .007 .027 .057 .096 .141 .189 .239 .288 .334 .375 .408 .432 .444 .441 .422 .384 .325 .243 .135 3 .000 .000 .001 .003 .008 .016 .027 .043 .064 .091 .125 .166 .216 .275 .343 .422 .512 .614 .729 .857 n 4 p .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 r 0 .961 .815 .656 .522 .410 .316 .240 .179 .130 .092 .062 .041 .026 .015 .008 .004 .002 .001 .000 .000 1 .039 .171 .292 .368 .410 .422 .412 .384 .346 .300 .250 .200 .154 .112 .076 .047 .026 .011 .004 .000 2 .001 .014 .049 .098 .154 .211 .265 .311 .346 .368 .375 .368 .346 .311 .265 .211 .154 .098 .049 .014 3 .000 .000 .004 .011 .026 .047 .076 .112 .154 .200 .250 .300 .346 .384 .412 .422 .410 .368 .292 .171 4 .000 .000 .000 .001 .002 .004 .008 .015 .026 .041 .062 .092 .130 .179 .240 .316 .410 .522 .656 .815 n 5 p .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 r 0 .951 .774 .590 .444 .328 .237 .168 .116 .078 .050 .031 .019 .010 .005 .002 .001 .000 .000 .000 .000 1 .048 .204 .328 .392 .410 .396 .360 .312 .259 .206 .156 .113 .077 .049 .028 .015 .006 .002 .000 .000 2 .001 .021 .073 .138 .205 .264 .309 .336 .346 .337 .312 .276 .230 .181 .132 .088 .051 .024 .008 .001 3 .000 .001 .008 .024 .051 .088 .132 .181 .230 .276 .312 .337 .346 .336 .309 .264 .205 .138 .073 .021 4 .000 .000 .000 .002 .006 .015 .028 .049 .077 .113 .156 .206 .259 .312 .360 .396 .410 .392 .328 .204 5 .000 .000 .000 .000 .000 .001 .002 .005 .010 .019 .031 .050 .078 .116 .168 .237 .328 .444 .590 .774 n 6 p .01 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 r 0 .941 .735 .531 .377 .262 .178 .118 .075 .047 .028 .016 .008 .004 .002 .001 .000 .000 .000 .000 .000 1 .057 .232 .354 .399 .393 .356 .303 .244 .187 .136 .094 .061 .037 .020 .010 .004 .002 .000 .000 .000 2 .001 .031 .098 .176 .246 .297 .324 .328 .311 .278 .234 .186 .138 .095 .060 .033 .015 .006 .001 .000 3 .000 .002 .015 .042 .082 .132 .185 .236 .276 .303 .312 .303 .276 .236 .185 .132 .082 .042 .015 .002 4 .000 .000 .001 .006 .015 .033 .060 .095 .138 .186 .234 .278 .311 .328 .324 .297 .246 .176 .098 .031 5 .000 .000 .000 .000 .002 .004 .010 .020 .037 .061 .094 .136 .187 .244 .303 .356 .393 .399 .354 .232 6 .000 .000 .000 .000 .000 .000 .001 .002 .004 .008 .016 .028 .047 .075 .118 .178 .262 .377 .531 .735

Substance Abuse and Addiciton A Very Brief History Essay...

Substance abuse can include any substance or substances such as alcohol, illegal drugs, prescription drugs, over the counter drugs, cigarettes etc. Any and all of these can become addictive to people very quickly. For years, people believed that addiction was a willful vice that they do to themselves. For years is has been viewed as an individual problem instead of a social problem. Americans today have many different views than 100 years ago about addiction, alcohol and drugs. In the early days of the 19th century, it was only a dream that a drug could save a life. Today drugs are used for specific treatments of specific diseases. However, they are also a multi billion-dollar business both legal and illegal that is not only saving†¦show more content†¦The fourth pharmacological revolution was the development of the oral contraceptive, which contributed to the sexual revolution, beginning to occur in the 1950’s and has not yet been stabilized. With oral contraceptives , they are not being used to prevent or treat disease but were being used by people to gain chemical control over their bodies. This may have helped pave the way for attempts to control emotion and thoughts by using chemistry. Drinking is okay, but drunkenness is not. Alcohol use was widely accepted since the time of first settlements. Due to Protestant reformers they discovered that drunkenness was viewed as a serious problem, often punished by putting a man in stocks for such an offense. Clearly the blame was on the sinner, not the alcohol itself. The view of alcohol as a cause of serious problems began in America soon after the American Revolution. Some people even to this day view alcohol as the devil of the demon. The first psychoactive substance to become demonized in American culture was alcohol. It led the way for similar views concerning cocaine, heroin, and marijuana. We are referring to a tendency to view a substance as an active (sometimes almost purposeful) source of evil, damaging everything it touches. This causes society to simply view it as â€Å"bad† and to seek to eliminate it. History of Substance Abuse Prevention Temperance Movement: 1784 Dr. Benjamin Rush wrote a book, The

An Inspector Call Characters Eric Essay Example For Students

An Inspector Call Characters Eric Essay For my essay I chose Eric because of his difference in personality from the other protagonist. Eric is a young man who likes getting his own way and being the centre of attention. I said this because of this quote Look here Ive had enough of this, which shows that he willing to take control of a situation and impose his views on others. The quotes call the audience attention. At beginning of act one, all the characters are quite enjoying Sheila engagement with Gerald. In this act Eric begins to laugh uncontrollably and rises from his chair (Suddenly guffaws), Sheila question what he is laughing about he replies that he just felt the need to laugh, Sheila calls him squiffy. Erick provokes her sister and she calls him an ass , at which point Mrs. Birling tells the two of them to stop it. (in this act Eric is acting strangely for reasons we dont know yet but we will know with play progresses) When he is first introduced in the opening stage directions. Were told that Eric is not quite at ease. He is apparently half shy and half assertive. During her sister engagement he interrupts Sheila and Gerald when he suddenly guffaws and when Sheila ask him why hes laughing but he says he doesnt know why hes laughing . He finds things his family say funny , even when theres no joke this shows that he was drunk. Hes quite noisy when he tells Gerald that Sheilas got temper he was probably drunk, Hes in an excitable , silly mood according to his mum. Eric get mad/paranoid when Gerald and his dad make the joke about his dads knighthood. Gerald says unless Eric is been up to something, and Eric acts suspiciously and seriously he says I dont think its very funny. He says still uneasy, and also answer defiantly. During Sheila and Gerald Dinner seems to be Nervous , irresponsible, inappropriate, drunk and unstable. Sheila realized he drinks a bit, but no one in the family really realises how messed up Eric really is , firstly hes a drinker a heavy drinker , and he has been for a while , we can see Erics familiarity with quick heavy drinking in the way he pours his whisky in Act three. The rest of the family sees it too. His family doesnt care about him , his dad sees him as a boy still. We get the the feeling he wishes Eric was a bit like Gerald, his dad also seems to be regret paying for his schooling particularly when Eric makes comment that show sympathy for the workers instead of the bosses . Mr Birling says angrily: its about time you learnt to face a few responsibilities Mr Birling is more worry  about his business and social scandal. Sheila seems to care about Eric , but mostly seems to pity him because hes I a mess. She doesnt really try to help him , she just says I dont want to get poor Eric into trouble but otherwise her Husband Gerald treats Eric like a younger brother. In act three Erics mums says Im absolutely ashamed of you. He is angry with her for turning Eva Smith away from her charity, and effectively killing her grandchild. He yells, Damn you, damn you and gets quite aggressive with her: (almost threatening her) You dont understand anything. You never did. You never even tried. Poor Eric no one likes him or knows him because his family only care about appearances not happiness . Eric is irresponsible, an alcoholic who sleeps with prostitutes, Eric is an alcoholic , Eva smith was a prostitute. Eric got her pregnant and he remembers very little about it . He has stolen money from his fathers business to support her. .u56028c32b2a6e2d5790c2877b0097ccb , .u56028c32b2a6e2d5790c2877b0097ccb .postImageUrl , .u56028c32b2a6e2d5790c2877b0097ccb .centered-text-area { min-height: 80px; position: relative; } .u56028c32b2a6e2d5790c2877b0097ccb , .u56028c32b2a6e2d5790c2877b0097ccb:hover , .u56028c32b2a6e2d5790c2877b0097ccb:visited , .u56028c32b2a6e2d5790c2877b0097ccb:active { border:0!important; } .u56028c32b2a6e2d5790c2877b0097ccb .clearfix:after { content: ""; display: table; clear: both; } .u56028c32b2a6e2d5790c2877b0097ccb { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u56028c32b2a6e2d5790c2877b0097ccb:active , .u56028c32b2a6e2d5790c2877b0097ccb:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u56028c32b2a6e2d5790c2877b0097ccb .centered-text-area { width: 100%; position: relative ; } .u56028c32b2a6e2d5790c2877b0097ccb .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u56028c32b2a6e2d5790c2877b0097ccb .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u56028c32b2a6e2d5790c2877b0097ccb .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u56028c32b2a6e2d5790c2877b0097ccb:hover .ctaButton { background-color: #34495E!important; } .u56028c32b2a6e2d5790c2877b0097ccb .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u56028c32b2a6e2d5790c2877b0097ccb .u56028c32b2a6e2d5790c2877b0097ccb-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u56028c32b2a6e2d5790c2877b0097ccb:after { content: ""; display: block; clear: both; } READ: English Coursework - An Inspector Calls EssayEric doesnt have many friends people to talk to give him an advise, his family certainly arent on his side, in fact no one seems to be on his side. He feels isolated and unsupported, hes had a neglected childhood and has had to find comfort elsewhere. He gets the readers sympathy because he and Sheila differ from their parents , Sheila refers to them as these others who are uncaring and insensitive, he also gets our sympathy because he sticks up for the workers and hes obviously a bit of a mess. During the play Eric recognize is mistakes , take responsibility for them , and learning from them. And he does seem to do that. He accuses the other of pretending nothings happened and he says you lot may be letting yourselves out nicely, he acknowledges he stole money and tells Gerald , Eric knows the moneys not the important thing. He knows that the life of the girl is more important than that unlike his father and mother , he gets depressed that his parents seem to be having cosy chat about it. By the end of play he accepts responsibility for what he did the fact remains that I did what I did

Public debt Essay Example

Public debt Essay Investigating the relationship between public debt and economic growth the case of Portugal Investigating the relationship between public debt and economic growth CAMPUS. The case of Portugal 11,499. The Implications of public obligation on economic growth are very Important to be researched as background to economic policies of a country. A country partly based on the comprehension of the relationship between public debt and economic growth to identify countries situation and draw specific plan to run a sound public debt policy for economic development. Therefore, a research into factors in which the amount of public debt affects the determinants of economic growth is necessary for a country to find out the situation of public debt and how to maintain its sound level to promote the economy. This research uses regression analysis model to examine the relationship between economic growth and public debt in case of Portugal with respect to factors such as investment and monetary policies. In which, Investment Is represented by foreign investment and domestic capital meanwhile, monetary policies are indicated by Inflation rate. With respect to research methodology, the research conducts literature review regarding both theoretical and emplace background and uses secondary data as data collection method and quantitative method as the research method. The process of data collection is implemented through data gathered from the official resources of WEB and COED including real GAP, public debt, inflow FED, inflation rate and annual capital growth in Portugal for the period 1992 to 2002. We will write a custom essay sample on Public debt specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Public debt specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Public debt specifically for you FOR ONLY $16.38 $13.9/page Hire Writer After conducting data analysis and regression analysis, the research findings shows that four variables namely public debt, foreign direct investment, monetary policy and investment have influences on economic growth demonstrated through GAP indicator. In the case of Portugal, public debt and foreign direct investment have positive relationship with GAP, while monetary policy and investment have negative Influence in GAP. Among those variables, public debt Is the most significant predictor at 32 level of significance. After findings, analysis and discussion, the research also comes to an end with several recommendations for Portugal based on the research findings on he Portugal case as well as some implications for further researches. First and foremost, my appreciation goes to all those who offer such a golden opportunity to conduct this graduation paper. I would like to thank () for giving me permission to implement the paper. I owe a debt of gratitude to my supervisor, 0, (. ). Without her/his enthusiastic guidance, persistent help and valuable encouragement, this paper would not have been possible.