This is true not only of GNU software, but also of a great deal of proprietary and free software.

I am dedicating this to my high-school teacher, Mr. I still remember finding the answer through some awkward method, just like the rest of the class did.

Only after simplifying the result did it occur to me that there should be an easy solution. Give it a fair shot before peeking! It's also the number of ways an n-sided convex polygon can be triangulated using only nonintersecting diagonals.

For a random sample of spacers, find the probability that: None of the spacers are defective. Three or more of the spacers are defective. Adding the above three results, we see that 2 or less spacers are defective with a probability of about Therefore, 3 or more are defective with a probability of about In a sample of n spacers, the average number of bad spacers is n times the probability of a bad spacer.

As usualobserve that "2 children have the same birthday" when 3, 4, or 5 do If we assume each kid has one of equiprobable birthdays, it's easier to compute the probability that they all have different birthdays: Now, let's bring leap years and February 29 into the picture.

We may even afford the luxury of using the full Gregorian calendar century years are not leap years except when divisible by ; was a leap year, was not. This is appropriate only when we do not know at what time the family lived for a 20th or 21st century family the Julian odds of exactly one leap year in 4 are more appropriate since was a leap year.

The Julian probability of having one's birthday on Feb. To this, we should add the probability that at least 2 kids were born on Feb. That's exactly chances in To summarize, the desired probability is about: Does this result apply to 5 siblings? No, it does not. Heck, it doesn't even apply to a random group of real people, because maternity wards are notoriously busier at certain times of the year Various additional statistical biases apply to siblings.

One major observation is that twins are not so rare, especially among large families. A minor observation is that the same woman cannot give birth in March and June of the same year For completeness, two people born on the same day of the same year may have the same mother, even if they're not twins.

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. Without loss of generality, we'll assume that the variance of U is 1. How do you work this out?

If n independent random samples are either equal to 1 with probability p or to 0 with probability 1-pthe sum of their values is a random variable which is said to have a binomial distribution; its average is np and its variance is np 1-p.

The standard deviation is the square root of this, roughly 7. The explanation for this simple formula repays study.

To obtain a binomial distribution both in theory and in practiceyou may consider the sum Y of n independent random variables X1, X2, The expectation E is a linear function. The last equality in this relation is known as Koenig's theorem. It is obtained simply by noticing that E Y is just a constant number.

The expectation of a constant number is itself and the expectation of a random variable multiplied by any constant number is simply that constant number multiplied by the expectation of the random variable.() The Monty Hall Paradox In a game-show, the contestant wins if he guesses correctly which one of three doors hides the (only) prize.

The rules of the game state that the contestant makes a tentative guess and is then shown one wrong choice among the two doors which he did not pick. The IEEE standard only specifies a lower bound on how many extra bits extended precision provides.

The minimum allowable double-extended format is sometimes referred to as bit format, even though the table shows it using 79 ph-vs.com reason is that hardware implementations of extended precision normally do not use a hidden bit, and so would use 80 rather than 79 bits.

Write an equation in standard form with integer coefficients for the line with slope 14/13 going through the point (-3,-1) Write an equation in standard form with integer coefficients for the line with slope 14/13 going through the point (-3,-1) Related Answers Using system of equation to solve.

() The Monty Hall Paradox In a game-show, the contestant wins if he guesses correctly which one of three doors hides the (only) prize. The rules of the game state that the contestant makes a tentative guess and is then shown one wrong choice among the two doors which he did not pick.

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial ph-vs.comly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and is written (). It is the coefficient of the x k term in the polynomial expansion of the binomial power (1 + x) n, and it is given by the formula =!!(−)!.

Write an equation in standard form with integer coefficients for the line with slope 13/19 going through the point (-2,-1) What is the equation of the line Start with the point/slope equation: y - y1 = m(x - x1).

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