Problem3: [Systems of Linear Equations] Determine which of the following equations are linear.

1. $x_1+2x_1x_2+3x_2=4$

2. $\sqrt{x_1}+3x_2=4$

3. $2x_1^{-1}+\sin x_2=0$

4. $3x_1-x_2=x_3+1$

Solution:

1. Not linear - contains non linear term $x_1x_2$

2. Not linear - contains non linear term $\sqrt{x_1}$

3.Not linear - contains non linear term $x_1^{-1}$

4. Linear - in the form of $a_1x_1 + a_2x_2 + .... + a_nx_n = b$

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Problem 105: If a bank receives on the average α = 6 bad checks per day, what are the probabilities that it will receive (a) 4 bad checks on any given day?
(b) 10 bad checks over any 2 consecutive days?

Problem 105: If a bank receives on the average α = 6 bad checks per day, what are the probabilities that it will receive (a) 4 bad checks on any given day? (b) 10 bad checks over any 2 consecutive days? Solution: Poisson distribution, $f(x;\lambda )=\frac{{\lambda }^{x}{e}^{-\lambda }}{x!}$ a. 4 bad checks on any given day Given that $x=4, \lambda = \alphaT = 6\dot 1 = 6$ $f(4;6 )=\frac{{6 }^{4}{e}^{-6 }}{4!} = 0.134$ b. 10 bad checks over any 2 consecutive days Given that $x=10, \lambda = \alphaT = 6\dot 2 = 12$ $f(10;12 )=\frac{{12 }^{10}{e}^{-12 }}{10!} = 0.104837$

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a. none of the buildings that violate the building code?
b. 1 of the new buildings that violate the building code?
c. 2 of the new buildings that violate the building code?
d. at least 3 of the new buildings that violate the building code?

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a. the formula for the hypergeometric distribution;
b. the formula for the binomial distribution as an approximation.

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