Explanation : Sample Space: It is a set of all possible outcomes of an experiment. It is usually represented as S. For example, if the random experiment is rolling of a die, the sample
space is a set, S = [1, 2, 3, 4, 5, 6].
Similarly, if the random experiment is tossing of three coins, the sample space is, S = [HHH, HHT, HTH, THH, HTT, THT, TTH, TTT] with total of 8 possible outcomes. (H is heads,
and T is Tails showing up.)
If we select a random sample of 2 items from a production lot and check them for defect, the sample space will be S = [DD, DS, DR, RS, RR, SS] where D stands for defective, S
stands for serviceable and R stands for reworkable.
Explanation : Binomial Distribution: The binomial distribution is usually exemplified by flipping a coin. The result can have only two outcomes, heads or tails, each of which has equal probability. The probability of either outcome remains the same throughout the experiment. The binomial distribution therefore describes the probability that in a finite number of trials (coin flips), there will be a specified number of heads (successes) or a specified number of tails (failures). The general form of the binomial distributions is
where n is the number of trials, r is the number of successes.
Explanation : Properties of Regression Coefficients:
Following are the important properties of Regression Coefficients:
> Same sign: Both regression coefficients have the same signs, i.e., either they will be positive or negative.
> Both can not be greater than one: If one of the regression coefficients is greater than unity, the either must be less than unity to
the extent the product of both regression coefficients is less than unity. In other words, both the regression coefficients cannot be greater than one.
> Independent of origin: Regression coefficients are independent of the origin but not of scale.
> A.M. > r: Arithmetic mean of regression coefficients is greater than the correlation coefficient.