The axial compressive load, X (measured in kN or kilo-Newtons), to be considered for the design of a column in a residential building has a probability density function (PDF), fjr(X), as follows: 0; x4 The mean of X is known to be 2 kN. (i) What are the values of a and 11? (ii) Draw a neat sketch of the PDF of X. (iii) Determine valid expressions for the cumulative distribution function (CDF) of X over the entire range from 00 to 00 in the same way as the PDF was expressed above, using the values of aand byou found. (iv) Draw a neat sketch of the CDF of X that you derived in (iii). (v) What is the median of X based on the CDF that you found? (vi) Use any method to find the 90th percentile value (X03) of X. (vii) What is the probability that the load exceeds 1.5 kN? (viii) If the load exceeds 1.5 kN, what is the probability that also exceeds 2 kN