STA301 Final Term Short Notes

STA301 Short Notes (23 to 45) Final Term By Junaid

Statistics and Probability (Virtual University of Pakistan)

Studocu is not sponsored or endorsed by any college or university

STA301 Short Notes (23 to 45) Final Term By Junaid

Statistics and Probability (Virtual University of Pakistan)

Studocu is not sponsored or endorsed by any college or university

STA301 SHORT NOTES

 Chebychev’s Inequality:

If X is a random variable having mean µ and variance σ2 > 0, and k is any positive constant, then the probability that a value of X falls within k standard deviations of the mean is at least.

 CONTINUOUS RANDOM VARIABLE:

A random variable X is defined to be continuous if it can assume every possible value in an interval [a, b], a < b, where a and b may be –∞ and +∞ respectively.

 JOINT DISTRIBUTIONS:

The distribution of two or more random variables which are observed simultaneously when an experiment is performed is called their JOINT

 BIVARIATE PROBABILITY FUNCTION:

The joint or bivariate probability distribution consisting of all pairs of values (xi, yj).

 MARGINAL PROBABILITY FUNCTIONS:

The point to be understood here is that, from the joint probability function for (X, Y), we can obtain the INDIVIDUAL probability function of X and Y. Such individual probability functions are called MARGINAL probability functions.

 CONDITIONAL PROBABILITY FUNCTION:

Let X and Y be two discrete r.v.’s with joint probability function f(x, y). Then the conditional probability function for X given Y = y, denoted as f(x|y).

 INDEPENDENCE:

Two discrete r.v.’s X and Y are said to be statistically independent, if and only if, for all possible pairs of values (xi, yj) the joint probability function f(x, y) can be expressed as the product of the two marginal probability functions.

 COVARIANCE OF TWO RANDOM VARIABLES:

The covariance of two r.v.’s X and Y is a numerical measure of the extent to which their values tend to increase or decrease together. It is denoted by σXY or Cov (X, Y), and is defined as the expected value of the product.

 BINOMIAL DISTRIBUTION:

The binomial distribution is a very important discrete probability distribution. It was discovered by James Bernoulli about the year 1700.

 PROPERTIES OF A BINOMIAL EXPERIMENT:

• Every trial results in a success or a failure.
• The successive trials are independent.
• The probability of success, p, remains constant from trial to trial.
• The number of trials, n, is fixed in advanced.

 Binomial probability distribution:

A probability distribution showing the probability of x successes in n trials of a binomial experiment.

 Binomial probability function:

The function used to compute probabilities in a binomial experiment.

 Binomial experiment:

A probability experiment having the following four properties: consists of n identical trials, two outcomes (success and failure) are possible on each trial, probability of success does not change from trial to trail, and the trials are independent.

 PROPERTIES OF A BINOMIAL EXPERIMENT:

• Every item selected will either be defective (i.e. success) or not defective (i.e. failure)
• Every item drawn is independent of every other item