In: Statistics and Probability
Assume that a continuous random variable has a following probability density function:
f ( x ) = { 1 10 x 4 2 ≤ x ≤ 2.414 0 o t h e r w i s e
Use this information and answer questions 3a to 3g.
Question a: Which of the following is a valid cumulative density function for the defined region ( 2 ≤ x ≤ 2.414)?
A.F x ( x ) = 1 50 x 5 − 16 25F x ( x ) = 1 50 x 5 − 16 25
B.F x ( x ) = 1 50 x 5F x ( x ) = 1 50 x 5
C.F x ( x ) = 3 10 x 4F x ( x ) = 3 10 x 4
D.F x ( x ) = 3 10 x 3 − 3 25F x ( x ) = 3 10 x 3 − 3 25
Question B: What is the probability that X is 2.4?
Question C: What is the probability that X is greater than 2.2 (use 3 decimal places)?
Question D: What is the probability that X is between 1.5 to 2.4? (use 3 decimal places)
Question E: What is the expected value of X? (use 3 decimal places)