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Using the Kuhn - Tucker conditions solve the following N.L.P.P. Maximize $z = 2x_{1} + 3x_{2} - x_{1}^2 - 2x_{2}^2$ Subject to $x_{1} + 3x_{2} \leq 6, 5x_{1} + 2x_{2} \leq 10, x_{1}, x_{2} \geq 0$.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Using the method of Lagranje's multipliers solve the given N.L.P.P. Optimize $z = 6x_{1}^2 + 5x_{2}^2$ Subject to: $x_{1} + 5x_{2} = 7, x_{1}, x_{2} \geq 0$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A continuous random variable x has the pdf defined by f(x) = A +Bx , 0 $\boldsymbol{\mathrm{\le}}$ x $\boldsymbol{\mathrm{\le}}$ 1 if mean of the distribution is 1/3. find A and B.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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The ratio of the probability of 3 successes in 5 independent trails to the probability of 2 successes in 5 independent trials is 1/4. What is the probability of 4 successes in 6 independent trials?
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A group of 10 rat fed on diet A and another group of 8 rat fed on different diet B , recorded the following increase in weight
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A continuous random variable has probability density function $f(x) = 6(x - x^2) 0 \leq x \leq 1$. Find mean and variance.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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If 10\% of bolts produced by a machine are detective. Find the probability that out of 5 bolts selected at random atmost one will be defective.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Based on the following data, can you say that there is no relation between smoking and literacy.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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The probability density function of a random variable x is :
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Out of 10 counters in a bag, 6 are 5 rupees each while the remaining 4 are of equal, but unknown value. If expectation of drawing a single counter at random is 4 rupees, find unknown value.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Monthly salary in a organization is normally distributed with mean rs. 3000, & s.d. of rs. 250. What should be the minimum salary of a worker so that the probability that he belongs to top 5% workers.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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The following table gives the number of accidents in a city during a week. Find whether the accidents are uniformly distributed over a week, using x$^{2}$ test.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A die was thrown 132 times and the following frequencies were observed, No. obtained: 1, 2, 3, 4, 5, 6. Frequencies: 15, 20, 25, 15, 29, 28. Total: 132 Test the Hypothesis that the die is unbiased.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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For a normal variate with mean 2.5 and S. D. 3.5 find the probability that 1) $2 \mathrm{\le} x \mathrm{\le} 4.5$ 2) $-1.5 \mathrm{\le} x \mathrm{\le} 5.5)$.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A sample of 50 pieces of certain types of string as tested. The mean breaking strength turned out to be 14.5 pounds. Test the following.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Table below shows the performance of students in Mathematics and Physics. Test the hypothesis that the performance in Mathematics is independent of performance in physics.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A random sample of 900 items is found to have a mean of 65.3cms, Can it be regarded as a sample from a large population whose mean is 66.2 cms and s.d. is 5 cms at 5% level of significance.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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In a laboratory experiment on two samples gave the following results.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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The weights of 4000 students are found to be normally distributed with mean 50 kgs & s.d. 5kgs. Find probability that a student selected at random will have weight i) $< 45$kgs. ii) between 45 & 60 kg
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A random variable X follows a poison distribution with variance 3 calculate p(X = 2) and p(X $\boldsymbol{\mathrm{\ge}}$ 4).
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Two independent samples of sizes 8 and 7 gave the following results.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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A continuous random variable with P.D.F f(x) = kx(1 - x), 0 $\mathrm{\le}$ x $\mathrm{\le}$ 1. Find K and determine a number ab such that P(x $\mathrm{\le}$ b) = p(x $\mathrm{\ge}$ b).
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Can it be concluded that the average life span of an Indian is more than 70 years, if a random sample of 100 indians has an average life span of 71.8 years with the standard deviation of 7.8 years.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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Tests made on breaking strength of 10 pieces of a metal wire gave the following results. 578, 572, 570, 568, 572, 570, 572, 596 and 584 in kgs. Test if the breaking strength of the metal wire can be a
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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In a test given to two groups of students drawn from two normal population marks obtained were as follows,
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
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