Assume that a continuous random variable has a following probability density function: f ( x )...

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)

Solutions

Expert Solution

thank you.

orchestra answered 1 year ago

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