Applied maths for electronics engineers june 2013 (2)
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This document contains two parts: Part A provides examples of classifying fuzzy propositions and different types of fuzzy quantifiers. Part B presents four mathematical problems: 1) determining the QR decomposition of a matrix, 2) finding the Cholesky decomposition of a matrix, 3) calculating properties of the Poisson distribution and finding moments of a given random variable, 4) solving problems related to the normal distribution including finding probabilities and the probability density function of a function of a Gaussian random variable.
Applied maths for electronics engineers june 2013 (2)
- 1. PART B- (5 x 16 = 80 marks) IX. /a) Explain: the classificataon of fuzzy'propositions with suitable examples. Or fm (i) What type of operators are used in Fuzzy expressions? (Ii) Explain the different types of fuzzy quantifiers with examples. [ -4 COLEtruct a QR decomposition for the matrix A = 3 6 2 -3 6 Or (LU Dater.mine the Cholesky decomposition for the given matrix (16 -3 5- -8 '-3 16 -5 -8 A=, 5 -5 24 0 l-s -8 0 21 TIl_ (aJ (1) Find the MGF of the Poisson distribution and hence find its mean and variance. (Ii) Fmd the first three moments of X if X has the following -"'''''-~~"''''--~iitii&iitimi: z.; -2 1 3 p(x): 1 1 1 244 Or (h) (i) The life of certain kind of electronic device has a mean of 300 hours and standard deviation of 25 hours. Assuming that the life times of the devices follownormal distribution, Find the probability that any one of these devices will have a life time more than 350 hours and what percentage will have life time between 220 and 260 hours? (:iii If Y =X2 , where X is a Gaussian random variable with zero mean and variance a'I.. find the probability density function, of the IMwdQm variable Y. .... "_'Ii. lIIi£. ~. Z % 2 2 .fall;. ~ JMRIiiWIP =.Yl + Ya + Ya ~iD YI+Y2+Y4~15 h~:!a,.:13~ o. Or 2 71486