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

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

When It Rains It Pours Essays - When It Rains, It Pours, Shine

When It Rains It Pours Essays - When It Rains, It Pours, Shine When It Rains It Pours As I sit here listening to it fall on my window sill I feel a shade of darkness come over me. I walk outside to feel it falling on me. As I life my face towards the heavens to feel it falling on me I have this dark feeling of dred. For me, rainy days and nights make me feel sad inside. I get depressed and want to stay in the house in bed. Whenever it rains I usually come downstairs and look out the window, only to see if my car is still in front of my door. As I stare at the sky, I think to myself, it's going to rain all day. But still, I thought, the sun could shine anyway, bringing with it the spring flowers that smell so lovely, the green grass, the blue sky, and the white clouds. Oh well, just a thought. I close my curtains and go back upstairs, I get back into bed and try to sleep. Sleep eludes me because I am thinking about things like life death, and money. It begins to pour and as the rain falls harder and hevier, I feel myself begining to fall asleep. Rain is like life, it comes and stays a while. Rain is like death, when it's time to stop it knows. Rain is also like money, when you have a lot of it, it pours. I dream of the day when the rain will go away, but until that day, I will listen to its drops on my window pane. Bibliography None needed

Analysis of Lewis Structures Research Paper Example | Topics and Well Written Essays - 750 words

Analysis of Lewis Structures - Research Paper Example The following are examples of the structures in a monoatomic form: Lewis structures are also used to indicate bonding in the form of a dash (-) for covalent bonds or a charge (+ or -) for ionic bonds (Schodek and Bechthold 301). Some examples: The bonds that are formed in the polyatomic structures usually have angles. The angles result in molecular geometry, which is best represented experimentally with the use of balls and sticks. The bonding angles that are involved in the analysis include linear, tetrahedral, trigonal pyramidal, trigonal planar, or bent. These are the geometries used in the Lewis structure experiments, though there are other geometric formations, where the structure does not adhere to the octet rule. Experimental Use The experimental representation of the Lewis structure requires the use of the following materials: A ball that has four holes, to be used as the central atom Inflexible sticks or straws for the single bonds a Flexible sticks or connectors for the dou ble or triple bonds The lone pairs around the central atom requires inflexible sticks NB: the balls used should be different in color as well as size to ease the representation of the elements and the electrons, with the central ball preferably larger. Arranging the experimental balls requires adherence to the guidelines for arranging the atoms, electrons, and bonds in the structures. Guidelines Involved In Using the Structures The rules in the experimental process of producing the Lewis structures follow these steps: 1. Draw the dot and structure diagram of the molecules or ions in question. For this step, knowledge on the bonds formed, their angles as well as geometry is important. The arrangement of the elements in the molecules is first established at this point. The central atom has to be established, the central atom, the element that holds most of the bonds is the structure. The following step to get involved into is the calculation of the valence bonds that are involved in t he bond formation, for a molecule (Schodek and Bechthold 501). The individual atoms and their configuration have to be considered in this case. The periodic table of elements is handy at this stage. The follow-up is the identification of bonds, following the octet rule i.e. a stable atom has to obtain a stable gas configuration in bond formation. 2. Determination of the overall and molecular geometry of the dot structure Using the knowledge of the geometry of formation, only as the octet rule applies, studying the dot structure allows inception of whether the structure is a linear, tetrahedral, trigonal pyramidal, trigonal planar, or bent formation. The main concept regarding the bond formation and geometry is the bond angles, which are 180 ° for the linear, 120 ° for the trigonal planar, 109.5 ° for the tetrahedral, 90 °, 120 ° and 180 ° for the trigonal by pyramidal, 90 ° and 180 ° for the Octahedral, etc (Schodek and Bechthold 492).  Ã‚