Computer Engineering Sem 4 Engineering Mathematics IV Question Paper PDF 2026 - Mumbai University | munotes
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Questions asked in this paper
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Q7 A continuous random variable X has the following probability density The function f(z) = has Poles of order 2 at of order3at z=1 Poles of order 2at z=1andapole of z=2 Poles of order 2 at of Poles of order 2 atz=1andapole of If the basic variable satisfies the non-negativity constraint, then solution is Based on the following data the calculated value of X is Solve any FOUR out of SIX. Each question carries 05 marks Verify Cayley-Hamilton theorem for the matrix A —1 4 | andhence find The average of marks scored by 32 boys is 72 with standard deviation 8 while that of 36 girls is 70 with standard deviation 6. Test at 1% level of significance whether the boys perform better than the girls Evaluate dz where C is the circle |z| = 3 Monthly salaries of 1000 workers have a normal distribution with mean 575 and a standard deviation of 75. Find the number of workers having salaries between 500 and 625 per month. Also find the minimum salary of the highest paid 200 workers E Use Kuhn Tucker Method to solve the NLPP F Determine all basic feasible solutions to the following problem
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Q3 (20 Solve any FOUR out of SIX. Each question carries C A discrete random variable has the probability density function given below Find k , mean and Variance Solve by Simplex Method Max z = 7x; + The sum of the squares of the deviations from the means are 26.94 and 18.73 respectively. Can the samples be considered to have been drawn from the same 5 marks
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Q4 (20_ | Solve any FOUR out of SIX. Each question carries Provethat A=|—8 3. is diagonalizable. Find the diagonal form D and the Find the Laurent’s series for f(z) = valid for 2 <3 C Fit a Poisson distribution to the following data Solve by Big M Method Max 3x, + 2X2 E A continuous random variable has the following probability density function 5 marks
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Q0 elsewhere Find m.g.f and hence find the mean and variance F The number of car accidents metropolitan city was found to be 20,17,12,6,7,15,8,5,16 and 14 per month respectively. Use test to check whether these frequencies are in agreement with the belief that occurrence of accidents was the same during 10 months period. Test at 5% level of significance
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