Question

2. Grafting, the uniting of the stem of one plant with the stem or root of another,is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with a hardy root system. Most Florida sweet oranges grow on trees grafted to the root of a sour orange variety. The density for X, the number of grafts that fail in a series of five trials, is given in the following table. x f(x) Table 1: My caption 0 1 2 3 0.7 0.2 0.05 0.03 4 0.01 5 ? List the elements of the sets corresponding to the following events: (a) Find f(5); (b) Find the table for CDF function F(x); (c) Sketch CDF function F(x); (d) Use F to find the probability that at most three grafts fail; that at least two grafts fail; (e) Use F to verify that the probability of exactly three failures is 0.03;

Answer 1

a)as sum of all sample point probability is 1

f(5) =1-0.7-0.2-0.05-0.03-0.01 =0.01

b)

x	0	1	2	3	4	5
F(x)	0.7	0.9	0.95	0.98	0.99	1

c)

F(x) 0 1 2 3 4 5 OF(x)

d)

P(At most 3 ) =F(3) =0.98

P(At least 2) =1-F(1) =1-0.9 =0.1

e)

P(exctly 3 failure) =F(3)-F(2) =0.98-0.95 =0.03