I need solve this assignment of IE230 - Probability & Statistics in Engineering I

Instructions for choosing your personally assigned values for Assessment 2 For Question 1 you will need your personally assigned Table Q1 t Table Q1 Number of Blemishes 0 2 3 5 (X) Probability f(x) 0.23 0.31 0.15 0.17 0.05 0.09 Page | 2 Question 1: Discrete random variables and distributions [50 points] The finishing process on new furniture leaves slight blemishes. The Table Q1 displays a manager's probability assessment of the number of blemishes in the finish of new furniture. Table Q1 [See page 2] Answer the following questions using your personally assigned Table Q1. a) Show that the function f(x) satisfies the properties of a probability mass function. [10 points] b) Determine the cumulative distribution function of the random variable X. [10 points] c) Find the mean (expected value), the variance, and the standard deviation of X. [15 points] d) Calculate the following probabilities: [15 points] 1. P(X> 3) P(X=6) AWN P(X2 3 UX 1 n X