Probability

No one "invented" it; it occurs naturally in a wide variety of real world situations. As for who discovered it and described it mathematically, that's another story.

The normal distribution is also known as the Gaussian distribution, after Johann Carl Friedrich Gauss (30 April 1777 to 23 February 1855). It was he first discovered the equations governing the distribution (in 1809) but saw it only as a tool for analysis of measurements. In 1810, Pierre-Simon, marquis de Laplace (23 March 1749 - 5 March 1827) proved its theoretical importance in math. But is was James Clerk Maxwell (13 June 1831 - 5 November 1879) who, decades later showed that the distribution also directly describes certain natural phenomena.

It is worth noting that Gauss, Laplace, and Maxwell each made numerous other contributions to mathematics and science, so one tends to see their names all over the place.

It is a certainty. There will always be at least one month that will meet the requirement.

6! =720

"Variance" and "Standard deviation" are numbers that describe a set of data

that typically contains several numbers. Applied to a single number, neither

of them has any meaning.

-- The variance, standard deviation, and mean squared error of 7 are all zero.

-- The mean, median, mode, average, max, min, RMS, and absolute value of 7 are all 7 .

None of these facts tells you a thing about ' 7 ' that you didn't already know

as soon as you found out that it was ' 7 '.

Probability are the odds of something happening but has multiple answers.

Such as probability of getting a 5 in a fair dice would be 1 out of 6 because there are 6 numbers on a dice altogether, and ONE chance of getting a 5 from the total of 6.

Therefore, the probability of getting a 5 or any number from a dice would be 1/6.

Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.

The probability is 11/36.

It refers to some variable whose distribution has got some mean and the measure of its spread is a standradr deviation of 17 cm. If the distribution is Normal (or approximately so), then the interval from the mean measure minus 17 cm to the mean plus 17 cm will contain approx 68% of the total number of observations.

When you throw a fair dice you have an equal possibility of getting 1, 2, 3, 4, 5 or 6. If you want to get a number greater than 4 this means you want 5 or 6: the probability is 2/6, which can be simplified to 1/3.

there are 38 slots on a US roulette wheel, (1-36, 0 and 00)

but they only payout 35 times your stake.

european tables have 37 slots but the same edge, if you do the maths american casinos have almost double the edge of european tables. like they need it...bit of a liberty if you ask me.

Getting heads is just as likely as getting tails.

So the expected number of each is even.

There are no other possibilities so you should expect 5 of each.

Naturally, if you actually flip a coin 10 times, it may come out 6/4, 4/6, 7/3 or even 10/0, but 5/5 is the most likely outcome.

Context of this question is not clear because it is NOT a full question. However

when attempting to estimate an parameter such as µ using sample data when

the population standard deviation σ is unknown, we have to estimate the standard

deviation of the population using a stastitic called s where

_

Σ(x-x)²

s = ▬▬▬▬

n -1

_

and estimator for µ , in particular x

........................................._

has a standard deviation of s(x)= s/√n

and the statistic

_

x - hypothesized µ

T = ▬▬▬▬▬▬▬▬▬▬

s

has a student's T distribution with n-1 degrees of freedom

If n> 30 , then by the Central Limit Theorem, the T distribution

approaches the shape and form of the normal(gaussian) probability

distribution and the Z table may be used to find needed critical statistical

values for hypothesis tests , p-values, and interval estimates.

Assuming you mean how many fours in a deck of playing cards, a standard deck has four. One heart, diamond, spade, clubs/

7*(1/2)7 = 7/128 = 5.47% approx.

Theorem

1/6+1/6=1/3

There are 10 different sets of teachers which can be combined with 4 different sets of students, so 40 possible committees.

You improve your model through a better understanding of the underlying processes.

Although more trials will improve the accuracy of experimental probability they will make no difference to the theoretical probability.

1/8.

The probability of flipping a coin three times and it landing on head is 1/2, as a coin only has two sides.

You flip a coin three times, therefore the answer is (1/2)^3 = 1/8.

50/50

That would depend upon what it is that is being rolled.

That would depend entirely upon what it is that is being rolled.

27 three digit numbers from the digits 3, 5, 7 including repetitions.

When you have independent events which have a constant probability of occurrence over an interval of space or time.

The answer depends on how many cards are picked. It is 1 if you pick 49 cards without replacement. If only one card is picked at random, the probability is 1/13.