what is the meaning of expectation and varience pls give some examples?

Answer 1

expectation is the mean value of what you would get if you did it loads of times.

varience is the mean value between the mean value and the real values you would get... if you did the experience loads of time...


Therefore: if you play a game and have an expectation of winning $1 and a variance of $3, then you can expect to win $1, but don't be surprised to lose $2 or win $4...

Answer 2

Ok... first off 'expectation' and the mean are two different things.

The 'expectation' is what you expect. Mathematically speaking the expected value of f(x) is

integral _ omega f(x) g(x) dx

Where omega is the support of x. g(x) is the density of x.

Complicated? Well not really thats just a very general idea.

Forget tha for now.

What about the mean?

Thats the population average and is calculated as the expected value of x

mu = E(x) = integral _ omega x g(x) dx

The mean is the 'center' of the distribution. (The average)

The variance is the centralized 2nd moment. WHA? Ok... well its this...

var = E[ (x - mu)^2] = integral _ omega [ x - mu ] ^2 g(x) dx

it is centralized since you took off mu which made it in the middle per se. The 2nd moment since it is a square power of x.

Variance is used to measure spread. The larger the variance is the more spread in the distribution. The smaller the closer the data is.

I could give examples... but thats a lot of work

Answer 3

If you are referring to statistical terms, read on; otherwise, I've no clue what you are asking.

Expected value (your expectation?) is defined as the probability of an outcome times the number of trials (attempts) at getting that outcome. In math talk, expected value = E(o) = P(o) X N(o); where P(o) is the probability of o (the desired outcome) and N(o) is the number of times or attempts at getting that outcome. So E(o) is the number of times you can "expect" to get o out of N(o) attempts.

Variance is a measure of how the outcomes you get spread out over a range of values. In math talk, variance = V(o) = Sum(o - m)^2/N(o); where (o - m) is the difference between each outcome and the average (m) of all outcomes. Summing up the square of each difference (there will be one term for each attempt) ensures variance will always be non negative. So the larger V(o) becomes, the greater that spread of values in outcome.

EXAMPLES: A pair of dice.

The expected value of rolling a pair of dice 100 times, when our point is a 2. E(2) = P(2) N(2) = (1/36) 100 = 100/36 = 25/9 With a pair of fair dice, there are 36 possible combinations of dots. Of those 36 possible outcomes, there is only one way to get the 2...you have to roll two ones, snake eyes. Thus, each time you roll a pair of dice, there is a 1 in 36 chance of rolling snake eyes. That is the probability of rolling a 2. In this example, you can expect to get your point (the 2) slightly less than three times (25/9) in those 100 rolls of the bones.

Variance is a bit trickier and beyond the scope of this answer. But if you take it on faith, the average point (outcome value) is 7 with a pair of fair dice. So each (o - m) term would look like (o - 7); where each o would be the value of each throw of the two dice and m, the average, would always be 7. So your variance would be V(o) = Sum(o - 7)^2/100 for 100 tosses of the dice; you would have to record the point (o) you rolled each time. As you can see, if you rolled the dice 100 times, you would have 100 terms in the summation. Again, taking it on faith, if your dice are fair, variance should come out about 2.0^2 = 4.

By the way, most analysts use the square root of variance to measure the spread of values. That square root of V(o) is called standard deviation. In the example, sqrt(V) = sqrt(4) = 2 for a pair of fair dice.

Answer 4

www.plmsc.psu.edu/~www/matsc597/probability/expectations/expectations