Question

X is a discrete random variable representing number of conforming parts in a sample and has following probability mass function

?(?) = { ?(5 − ?) if ? = 1, 2, 3, 4

0 otherwise

i) Find the value of constant ? and justify your answer

. ii) ( Determine the cumulative distribution function of X, (in the form of piecewise function).

iii) Use the cumulative distribution function found in question 2 to determine the following:

a) ?(2 < ? ≤ 4)

b) ?(? ≥ 3)

Answer 1