a'bivariate distriuition Given biloe s for the randen Variables n andy, 90 20 20 40 70 Compute the covcriance cnd corelation for n and
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Introduction:
Suppose X and Y are two discrete random variables with probability mass functions (pmf) f (x) and f (y), and joint probability mass function f (x, y).
Then, the covariance between X and Y can be calculated using E (XY), the expectation of X that is E (X), and the expectation of Y that is E (Y) using the formula:
The correlation coefficient between X and Y can be calculated using Cov (X, Y), the variance of X that is V (X), and the variance of Y that is V (Y) using the formula:
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