If random variable is normally distributed then it is a                     random variable.?
913220
b\nNormal distributions are always continuous.
272822
One cool way that I have seen it derived is based on Jayne's Formalism.\n\nAssume we sample process, and measure the mean and standard devation of the samples. There are many possible distributions that will produce those exact mean and standard deviation. \n\nJayne's Formalism chooses the distribution which maximizes the entropy of the distribuiton. This is viewed mathematically as the distribution that makes the minimum number of assumptions regarding the distribution.\n\nI always thought that was kinda cool.
794682
Suppose X is a continuous random variable whose density function f is defined by f(x) = x/2 whenever 0<x<2 and f(x) = 0 otherwise. Then,\nE[X] = integral (x * f(x), x=0..2 ) dx\n     = integral (x * x/2, x=0..2 ) dx\n     = (1/2) integral (x^2, x=0..2 ) dx\n     = [(1/6)*x^3, x=0..2] \n     = (1/6)*2^3 - (1/6)*0^3 \n     = (8/6)\n     = (4/3).\n\nNext, \nE[ | X - E[x] | ] = E[ | X - 4/3 | ] \n     = integral ( | x - 4/3 | * f(x), x=0..4/3 ) dx + integral ( | x - 4/3 | * f(x), x=4/3..2 ) dx\n     = integral ( - (x - 4/3) * f(x), x=0..4/3 ) dx + integral ( (x - 4/3) * f(x), x=4/3..2 ) dx\n     = integral ( (4/3 - x) * x/2, x=0..4/3 ) dx + integral ( (x - 4/3) * x/2, x=4/3..2 ) dx\n     = integral ( (2/3)x - (1/2)x^2), x=0..4/3 ) dx + integral ( (1/2)x^2 - (2/3)x, x=4/3..2 ) dx\n     = [(1/3)x^2 - (1/6)x^3, x=0..4/3 ] dx + [(1/6)x^3 - (1/3)x^2, x=4/3..2]\n     = ( (1/3)(16/9) - (1/6)(64/27) - 0 + 0) + ( 8/6 - 4/3 - (1/6)(64/27) + (1/3)(16/9))\n     = ( 16/27 - 32/81 ) + ( 16/27 - 32/81 )\n     = 2(16/27 – 32/81)\n     = 32/81.\n\n--- \n\nSome notation used:\nintegral (f(x), x = a..b) dx means we evaluate the definite integral of f(x) bounded by x = b and x = a.\n\n[ F(x), x =  a.. b ] means we evaluate the difference, F(b) - F(a).\n.
478561
I don't remember N value, but I know that P value is the probability that something is done by "chance".  In other words, I cannot "prove" that I am a psychic, but I can do things that point farther and farther away from me 'cheating" or "just guessing".  The farther one gets from something being "chance" the smaller the P value is.  In Statistics, P-value is only considered "significant" if it is below .05 (or less than possibly happening one in 20 times).
403633
If by infinite randomness you mean true randomness, then I don't think it can. All random generators are programmes that follow an algorithm to produce 'random' results. Whilst for most purposes the result is sufficiently random to be useful, they are not as random as, for example, drawing lottery numbers.
119401
Yes, it's a function.  Each x-value has only 1 y-value.
469250
Discrete Case:\nE[X] = Sigma_{i=1}^n x_i*p(X = x_i) \n\nwhere Sigma_{i=1}^n p(X = x_i) = 1\n\nContinuous Case:\nE[X] = int(x*p(X = x)dx,-infty,infty)\n\nThink of it as a weighted *average*.
887169
You're getting into logarithm.  If X/D = R^Y, then Y = log(X/D), where log is the logarithm in base R.
828433
A discrete variable typically fits into a category and is a yes or no answer.  They are tabulated into single events, i.e. broken = yes or no?.\n\nA continuous variable is something measured on a continuum, and can have an infinite number of values.\n\nA good test for this is to ask if it can be divided in half.  For example, Can something be half broken?  If is doesn't make sense to be, it is discrete.
221335
Standard deviation of a random variable X is defined as: \nό=√E((X-E(X))2) = √E(X2)-(E(X))2\n(the 2's of course are squares)
173519
I guess you are talking about the statistical significance, of the difference of two random variables (or functions of variables).\nThat would be the case, for example if you want to test whethern two means are or not equal.\nThen, the difference of the two means can be tested to be or not zero. For that, you need to know the distribution of the original variables.\nIf the two samples come from the same normal population and are of the same size, then the difference is normal with mean zero and variance = 2*sigma^2/n where n is the sample size.\nThen, if the value (In absolute terms) is greater than X(p) then they are significantly different with probability p.\nX(p) is such P(X>X(p))=1-p.
286964
If a random experiment has two possible outcomes, success with proability  p and failure with probability q=1-p. And the experiment is repeated until a success happens. The number of trials before the success is a random variable  with density function\nf(x)=q^(x-1) * p     is called the geometric distribution.\n\n\nhttp://library.thinkquest.org/10030/6dpdgd.htm\n\nhttp://en.wikipedia.org/wiki/Geometric_distribution
634372
Luck is when there is a deviation from expectation.  For example, Flipping heads twelve times in a row is lucky as one would expect to see heads only 6 times, given the probability of a heads (assuming we are tossing a fair coin).  A chance, by definition is something that is random.  Note, however, that in your question you have written "luck/chance" as those they were interchangeable.  They are not.  Lucky is when an event occurs when the chances are in fact small as determined by probability.\n\nAlso, there is no scientific evidence to suggest anything like Karma or Worldy energies affect chances of an event or your luck.  That's all just mumbo-jumbo.
947255
Let X be mean fill of container. \n\nThe distribution is X~N(16, 1.5) i.e. it is normally distributed as stated in the question.\n\nWant to find P(X>17), so standardise.\nP(X>17) = P(Z>(17-16)/(1.5/2)) = P(Z>1.33)\n\nThen you look up your normal table. The answer is approximately 0.09.
4416
No.  There are a lot of different types of distributions to model the many phenomena in the universe and in society.\n\nCheck out this list:\nhttp://en.wikipedia.org/wiki/Probability_distribution\nThe normal distribution is way down in the list somewhere!
205936
1) The natural logarithm started life as the integral of 1/t from 1 to x. This integral was defined to be the natural logarithm because it satisfied the properties of a logarithm in x. The base of this logarithm was called e, Euler's number. Describing the usefulness of this number, and thus why everyone accepted the term natural logarithm, fills several good books, but you can find a condensed version in the source link. \n2) A distribution which is log-normal may be written as a large sum over the logarithm of some random variable, and thus the logarithm of a product over that random variable. Consider the central limit theorem applied to the logarithm of a random variable. More information can be found in the source link below.
280200
If a random sample size of 25 corresponds to a standard deviation of 30, then you can expect a random sample of size 25N to roughly correspond to a standard deviation of 30 / sqrt(N).\n\nIf 99% of the area under the bell curve is between -Z and +Z standard deviations, then you want 30 Z / sqrt(N) to be less than or equal to 0.5.\n\nMaybe a little more because of the variation of the estimated standard deviation from the true standard deviation.\n\nAlso check that the theory and the measurements both suggest it is appropriate to use the normal or Gaussian distribution.