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Graphs and Functions

Point Estimation in Statistics

22. Let X denote the proportion of alloted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is ... a. Use method of moments to obtain an estimator ... b. Obtain the maximum likelihood esitmator ... Please see attachment for complete question. Thank you!

Quadratic Equation Pictured

A square picture is mounted in a frame 1 cm wide. The area of the picture is 2/3 of the total area. Find the length of a side of the picture.

Function solutions

2. Given the polynomial f(x) = 2x 3 -5x2-4x+3, find the solutions if the function is completed as a) f(x) =0 b) f(x+2)=0 d) f(2x) = 0

Prove A Variation of Fermat's Theorem

There always exists a real number n such that a^n = b^n + c^n , where a, b and c are any integers. The problem is not Fermat's Last Theorem, but a variation of it with real exponents.

Functions: Onto and One-to-one, Bijections and Functions

Please help with the following problems on graphs and functions. Provide step by step calculations. 1. Assuming A,B not equal to no solution, define m1:AxB->A and m2:AxB-> as follows: m1(x,y)=x and m2(x,y)=y. If f: A->B, show that a) f onto=>m2 |f is onto b)f one-to-one=>m2 f is one-to-one 2. Assuming f: A->B and g:

Functions and Graphs: Trends and Real World Implications

Plot your data for each disease as points in a rectangular coordinate system. Year...................1985..........1990..........1995......2002 Heart Disease 771,169 720,058 684,462 162,672 Cancer 461,563 505,322 554,643 557,271 AIDS * 8,000 25,188 39,979 14,095 - Use individu

Limit and Slope of Tangent Line, Midpoint and Trapezoidal Rule

Use the limit definition to find the slope of the tangent line, f(x)= X^2+2X+1 Use the midpoint rule to approximate the area of the function f(x)=-2x+3 from [0,1] when n=4. Compare this approximation to the actual area by integration to the approximate area using the trapezoid rule. Sketch the and find its average rate

Plotting a Surface Function

Consider the function u(x,t) = sin(4 pi x) e^(-pi t). Plot using a graphical tool and explain what you observe. Please see the attached file for the fully formatted problems.

Statistics

What is the "causal relationship" between independent and dependent variable?

Sequence of Functions and Mean Value Theorem

Let a<b. Let f_n: [a,b] -> R be a sequence of functions such that, for each n in N ( N set of natural numbers),f_n is differentiable on (a,b). Suppose that for all n in N, Sup on [a,b] of | f'_n(x) | < or = to M, where M is in R. ( Sup is supremum = least upper bound) Prove that for all n in N and all x, y in [a,b], one has

Uniformly Cauchy Sequence of Continuous Functions

Let f_n : [0,1] -> R be a sequence of continuous functions such that for each n in N (natural numbers), f_n is differentiable on (0,1). Suppose that f_n(0) converges to some number, denoted f(0), and also suppose that the sequence (f'_n) converges uniformly on (0,1) to some function g: (0,1) -> R. Prove that the sequence (f_n) c

Diffusion Equation : Energy Decreasing as a Function of Time

3. Suppose that u(x. t) satisfies the diffusion equation ut = kuxx for 0 < x < L and t > 0, and the Robin boundary conditions ux(0, t) ? aou(0, t) = 0 and ux(L, t) + aLu(L, t) = 0 where k, L, a0 and aL are all positive constants. Show that ... is a decreasing function of t. Please see the attached file for the fully for