f. the percentage change in going from y1 to y2 if log y1 = 1.82 and loge y2 = 1.79
g. the percentage point change in the unemployment rate when the rate goes from 6% to 9%
i. the percentage change in X when X goes from 2 to 0
j. the percentage change in X when X goes from 0 to
k, where k is a number greater than zero
Answer (f) 90.93467%
Explanation
Given
Log y1 = 1.82
This means that log has a base of 10
Taking Antilog of Y1 we get
Y1= 66.0693
Also,
Loge Y2 = 1.79
This means that log has base a of exponential (e)
Taking Antilog of Y2 we get
Y2 = 5.9894
Percentage from Y1 to Y2 = ((Y2- Y1)/Y1)*100
= ((5.9894 - 66.0693)/ 66.0693)*100
= -90.9347%
(g) Percentage point change is 9%-6% = 3%
Percentage change in X when X goes from 2 to 0
= (( 0-2)/2)*100
= -100%
Percentage change when X goes from 0 to k is
= ((k-0)/0)*100
Above ratio can not be calculated since denominator is 0
f. the percentage change in going from y1 to y2 if log y1 = 1.82 and...
Let Y1,Y2, …… Yn be a random sample from the distribution f(y) = θxθ-1 where 0 < x < 1 and 0 < θ < ∞. Show that the maximum likelihood estimator (MLE) for θ is
Let Y1<Y2<...<Yn be the
order statistics of a random sample of size n from the distribution
having p.d.f f(x) = e-y , 0<y<, zero elsewhere. Answer the following
questions.
(a) decide whether Z1 = Y2
and Z2=Y4-Y2 are
stochastically independent or not. (hint. first find the joint
p.d.f. of Y2 and Y4)
(b) show that
Z1 = nY1, Z2=
(n-1)(Y2-Y1),
Z3=(n-2)(Y3-Y2), ....,
Zn=Yn-Yn-1
are stocahstically
independent and that each Zi has the exponential
distribution.(hint use change of variable technique)
A standing wave results from the sum of two transverse traveling waves given by y1 = ymcos(kx - ωt) and y2 = ymcos(kx + ωt) where ym = 0.047 m, k = 3.2 rad/m, and ω = 12 rad/s. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t = 0, what is the value of the (b) first, (c) second, and (d) third time the particle at x = 0 has zero...
A standing wave results from the sum of two transverse traveling waves given by y1 = ymcos(kx - ωt) and y2 = ymcos(kx + ωt) where ym = 0.057 m, k = 4.4 rad/m, and ω = 13 rad/s. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t = 0, what is the value of the (b) first, (c) second, and (d) third time the particle at x = 0 has zero...
5. Consider a random sample Y1, . . . , Yn from a distribution with pdf f(y|θ) = 1 θ 2 xe−x/θ , 0 < x < ∞. Calculate the ML estimator of θ. 6. Consider the pdf g(y|α) = c(1 + αy2 ), −1 < y < 1. (a) Show that g(y|α) is a pdf when c = 3 6 + 2α . (b) Calculate E(Y ) and E(Y 2 ). Referencing your calculations, explain why M1 can’t be...
14. Percentage change Aa Aa An often-used percentage application in finance is the percentage change. Percentage changes are calculated as the change in value divided by the base value: New Value Base Value Base Value Percentage Change (%A) x 100% Suppose a stock traded for $40 a share last year, but today the price has risen to $44. In this case, the percentage change is: Percentage Change, %Δ-($44-$-40) / $40-10% If a stock price falls from $20 to $18.50, the...
14. Percentage change Aa Aa An often-used percentage application in finance is the percentage change. Percentage changes are calculated as the change in value divided by the base value: Percentage Change (%A) New Value Base Value Base Value x100% Suppose a stock traded for $40 a share last year, but today the price has risen to $44. In this case, the percentage change is: Percentage Change, 96 ($44 _ $40) / $40-10% If a stock price falls from $20 to...
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...
Suppose we are given two sorted arrays (nondecreasing from index 1 to index n) X[1] · · · X[n] and Y [1] · · · Y [n] of integers. For simplicity, assume that n is a power of 2. Problem is to design an algorithm that determines if there is a number p in X and a number q in Y such that p + q is zero. If such numbers exist, the algorithm returns true; otherwise, it returns false....
The following graph shows the relationship between real GDP growth and change in unemployment for the US between 1961 and 2013. US (1961-2013) y = -0.3768x +1.2298 R-0.641 Change in unemployment rate (%) -1 0 Real GDP growth (%) The equation shown is the regression result for the best-fitting line. Based on this information, which of the following statements is correct? a) With real GDP falling by 2.8% in 2009, the predicted rise in the unemployment rate would have been...