On a laboratory assignment, if the equipment is working, the density function of the observed outcome, X, is S 2(1 – æ), 0<æ < 1, f(x) = %3D 0, elsewhere Find the cumulative distribution function F(x). What is the probability that X will exceed 0.5?
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.
Please show the steps and answer both parts. If possible, show how this is solved using R. Thanks in advance! :)
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