Question

Consider the following cumulative probability distribution.

x	0	1	2	3	4	5
P(X ≤ x)	0.10	0.29	0.48	0.68	0.84	1

a. Calculate P(X ≤ 2). (Round your answer to 2 decimal places.)

b. Calculate P(X = 2). (Round your answer to 2 decimal places.)

c. Calculate P(2 ≤ X ≤ 4). (Round your answer to 2 decimal places.)

Answer 1

We calculate P(X = x) from cumulative frequency P(X <= x) as

P( X = x) = P( X <= x) - P( X <= x-1)

For example,

P(X =2 ) = P( X <=2 ) - P( X <= 1)  

= 0.48 - 0.29

= 0.19

X	0	1	2	3	4	5
P(X <= x)	0.10	0.29	0.48	0.68	0.84	1
P(X = x)	0.10	0.19	0.19	0.20	0.16	0.16

a)

P( X <= 2) = P (X = 0) + P (X = 1) + P (X = 2)

= 0.10 + 0.19 + 0.19

= 0.48

b)

P( X = 2) = 0.19

c)

P( 2 <= X <= 4) = P( X = 2) + P (X = 3) + P (X = 4)

= 0.19 + 0.20 + 0.16

= 0.55