Ejercicio #1 Resuelve la ecuación logarítmica log, x + log, 2 = 3 Ejercicio #2 Resuelve la ecuación logarítmica log, x + log2 (x − 2) = 3 Ejercicio #3 Resuelve la ecuación logarítmica In(6x – 3) – In(4.x – 1) = ln x

Ejercicio #1 Resuelve la ecuación logarítmica log, x + log, 2 = 3 Ejercicio #2 Resuelve la ecuación logarítmica log, x + log2 (x − 2) = 3 Ejercicio #3…

Continue Reading Ejercicio #1 Resuelve la ecuación logarítmica log, x + log, 2 = 3 Ejercicio #2 Resuelve la ecuación logarítmica log, x + log2 (x − 2) = 3 Ejercicio #3 Resuelve la ecuación logarítmica In(6x – 3) – In(4.x – 1) = ln x

Assume that a decision maker’s current wealth is 10,000. Assign u(0) = – 1 and u(10,000) = 0 When facing a loss of X with probability 0.5 and remaining at current wealth with probability 0.5, the decision maker would be willing to pay up to G for complete insurance. The values for X and G in three situations are given below. X c 10 000 6 000 61100 3 300 3 300 1 700 Determine three values on the decision maker’s utility of wealth function u. Calculate the slopes of the four line segments joining the five points determined on the graph u(w). Determine the rates of change of the slopes from segment to segment. Put yourself in the role of a decision maker with wealth 10,000. In addition to the given values of u(0) and u(10,000), elicit three additional values on your utility of wealth function u. On the basis of the five values of your utility function, calculate the slopes and the rates of change of the slopes as done in part (b).

Assume that a decision maker's current wealth is 10,000. Assign u(0) = - 1 and u(10,000) = 0 When facing a loss of X with probability 0.5 and remaining at…

Continue Reading Assume that a decision maker’s current wealth is 10,000. Assign u(0) = – 1 and u(10,000) = 0 When facing a loss of X with probability 0.5 and remaining at current wealth with probability 0.5, the decision maker would be willing to pay up to G for complete insurance. The values for X and G in three situations are given below. X c 10 000 6 000 61100 3 300 3 300 1 700 Determine three values on the decision maker’s utility of wealth function u. Calculate the slopes of the four line segments joining the five points determined on the graph u(w). Determine the rates of change of the slopes from segment to segment. Put yourself in the role of a decision maker with wealth 10,000. In addition to the given values of u(0) and u(10,000), elicit three additional values on your utility of wealth function u. On the basis of the five values of your utility function, calculate the slopes and the rates of change of the slopes as done in part (b).

In Problems 3–8, determine whether the given function is a solution to the given differential equation.

In Problems 3–8, determine whether the given function is a solution to the given differential equation. x=2cost Estimate the diffusivity of isoamyl alcohol (C,H120) at infinite dilution in water at…

Continue Reading In Problems 3–8, determine whether the given function is a solution to the given differential equation.

Find at least the first four nonzero terms in a powerseries expansion about x = 0 for a general solution to thegiven differential equation: Include a general formula for the coefficients (recurrence formula). x=0; (x^2 +4)y” + y=x

Find at least the first four nonzero terms in a powerseries expansion about x = 0 for a general solution to thegiven differential equation: Include a general formula for the…

Continue Reading Find at least the first four nonzero terms in a powerseries expansion about x = 0 for a general solution to thegiven differential equation: Include a general formula for the coefficients (recurrence formula). x=0; (x^2 +4)y” + y=x

A univariate Gaussian or normal distributions can be completely determined by its mean and variance. Gaussian distributions can be applied to a large numbers of problems because of the central limit theorem (CLT). The CLT posits that when a large number of independent and identically distributed (i.i.d.) random variables are added, the cumulative distribution function (cdf) of their sum is approximated by the cdf of a normal distribution. Recall the probability density function of the univariate Gaussian with mean u and variance o?, N (1, 02): fx (2) = 1 27102 (2–)*/(20) e Probability review: PDF of Gaussian distribution 2 points possible (graded) In practice, it is not often that you will need to work directly with the probability density function (pdf) of Gaussian variables. Nonetheless, we will make sure we know how to manipulate the (pdf) in the next two problems. The pdf of a Gaussian random variable X is given by n n2(x – 2) fx (2) exp 327 then what is the mean p and variance o2 of X? (Enter your answer in terms of n.) M= 02 Probability review: PDF of Gaussian distribution 1 point possible (graded) Let X~ N (4,02), i.e. the pdf of X is 1 (x – u)? fx (x) exp 027 202 Let Y = 2X. Write down the pdf of the random variable Y. (Your answer should be in terms of y, o and p. Type mu for sigma for o.) fy (y) = Argmax 1 point possible (graded) Let fx (x;j, o?) denote the probability density function of a normally distributed variable X with mean u and variance 02. What value of x maximizes this function? (Enter mu for the mean ji, and sigma-2 for the variance o?.)

A univariate Gaussian or normal distributions can be completely determined by its mean and variance. Gaussian distributions can be applied to a large numbers of problems because of the central…

Continue Reading A univariate Gaussian or normal distributions can be completely determined by its mean and variance. Gaussian distributions can be applied to a large numbers of problems because of the central limit theorem (CLT). The CLT posits that when a large number of independent and identically distributed (i.i.d.) random variables are added, the cumulative distribution function (cdf) of their sum is approximated by the cdf of a normal distribution. Recall the probability density function of the univariate Gaussian with mean u and variance o?, N (1, 02): fx (2) = 1 27102 (2–)*/(20) e Probability review: PDF of Gaussian distribution 2 points possible (graded) In practice, it is not often that you will need to work directly with the probability density function (pdf) of Gaussian variables. Nonetheless, we will make sure we know how to manipulate the (pdf) in the next two problems. The pdf of a Gaussian random variable X is given by n n2(x – 2) fx (2) exp 327 then what is the mean p and variance o2 of X? (Enter your answer in terms of n.) M= 02 Probability review: PDF of Gaussian distribution 1 point possible (graded) Let X~ N (4,02), i.e. the pdf of X is 1 (x – u)? fx (x) exp 027 202 Let Y = 2X. Write down the pdf of the random variable Y. (Your answer should be in terms of y, o and p. Type mu for sigma for o.) fy (y) = Argmax 1 point possible (graded) Let fx (x;j, o?) denote the probability density function of a normally distributed variable X with mean u and variance 02. What value of x maximizes this function? (Enter mu for the mean ji, and sigma-2 for the variance o?.)

A unit vector is a vector with length, or norm, 1. Given any vector x, what is the unit vector pointing in the same direction as x? (Enter norm(x) for the norm ∥x∥ of the vector x. In general, you can enter the norm of a vector using the norm function).

A unit vector is a vector with length, or norm, 1. Given any vector x, what is the unit vector pointing in the same direction as x? (Enter norm(x) for…

Continue Reading A unit vector is a vector with length, or norm, 1. Given any vector x, what is the unit vector pointing in the same direction as x? (Enter norm(x) for the norm ∥x∥ of the vector x. In general, you can enter the norm of a vector using the norm function).

Asymptotics and Trends 0.0/4.0 points (graded) For each of the following functions f (2) below: • Find its limits lim f(c) as x approachs too. 1-too • Choose the values of x where f(c) is differentiable, i.e. f’ (2) exists • Choose the values of x where f (x) is also strictly increasing, i.e. f’ (2) > 0. 1. For f(x) = max(0, 2): (If the limit diverges to infty, enter inf for oo, and -inf for – ) lim f(x) = lim f() = 1+0o Choose the intervals of x where f(x) differentiable: f'(x) > 0: (Choose all that apply.) 2 0 (Graph this function on a piece of paper!) 2. For f(x) = 1 1+e-2 (Enter inf for and similarly -inf for – if the limit diverges to infty.) lim f(x) = 1-00 lim f(x) = Too Choose the intervals of x where f'(x) > 0 f (2) differentiable: (Choose all that apply.) 2 0 (Graph this function on a piece of paper!)

Asymptotics and Trends 0.0/4.0 points (graded) For each of the following functions f (2) below: • Find its limits lim f(c) as x approachs too. 1-too • Choose the values…

Continue Reading Asymptotics and Trends 0.0/4.0 points (graded) For each of the following functions f (2) below: • Find its limits lim f(c) as x approachs too. 1-too • Choose the values of x where f(c) is differentiable, i.e. f’ (2) exists • Choose the values of x where f (x) is also strictly increasing, i.e. f’ (2) > 0. 1. For f(x) = max(0, 2): (If the limit diverges to infty, enter inf for oo, and -inf for – ) lim f(x) = lim f() = 1+0o Choose the intervals of x where f(x) differentiable: f'(x) > 0: (Choose all that apply.) 2 0 (Graph this function on a piece of paper!) 2. For f(x) = 1 1+e-2 (Enter inf for and similarly -inf for – if the limit diverges to infty.) lim f(x) = 1-00 lim f(x) = Too Choose the intervals of x where f'(x) > 0 f (2) differentiable: (Choose all that apply.) 2 0 (Graph this function on a piece of paper!)