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Expected value

The expected value of a random variable characterises its distribution by specifying a mean value. This does not have to occur among the values of the random variable itself.

It also makes sense to consider mean values for probability distributions - do my engineering assignment for me (as for frequency distributions). One such value is the expected value of a random variable, which characterises its distribution by a mean value.

Then the number is called

E (X)=x1⋅p1+x2⋅p2+...+xk⋅pk

the expected value of X.

The expected value need not occur (as the following examples show) among the values of the state variable.

Example 1:

The expected value of the random variable number of eyes A when throwing an ideal die is:

E (A)=1⋅16+2⋅16+3⋅16+4⋅16+5⋅16+6⋅16 =21⋅16=3.5

Example 2:

The dice are rolled with a loaded die. For the probability distribution of the number of dice A, let:

P(1)=29P(2)=P(3)=P(4)=P(5)=16P(6)=19

Thus, the expected value is

E (A)=1⋅29+2⋅16+3⋅16+4⋅16+5⋅16+6⋅19 =89+146=1618+4218=5818≈3.22 With the help of the expected value, it is possible to evaluate the winnings in a lottery sale or a
raffle.

Galton board

A Galton board is used to illustrate binomial distributions. It is named after the English naturalist Sir Francis Galton (1822 to 1911), a cousin of Darwin - same day essay writing . Galton was primarily an anthropologist and also constructed the so-called Galton pipe.

Binomial distributions, i.e. the sequence of Bernoulli chains, can be illustrated with the help of a Galton board. This is a board set up at an angle, on which there are obstacles (nails) arranged in k rows. Balls whose diameter is slightly smaller than the distance between the nails fall through a funnel onto the obstacles and are deflected by them - domyhomework club . A deflection to the right is considered a success, a deflection to the left a failure. If the distance between the nails is the same, the chance of being deflected to the right or to the left is the same (probability p is 0.5).

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