4 random process X (t) has an auto correlation functionRYx (t) = A2 + B. e-lt, where A and B are positive constants. Find the meanvalue of the response of a system having an impulse respònseh (t) = e-kt for t > 0= 0 for t< 0 .where K is a real positive constant, for which X (t) is its input.

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Answered: 4 random process X (t) has an auto…

MATLAB: An Introduction with Applications

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A catalog company builds a logistic regression (LR) model to predict the probability that a customer will buy from the catalog during a particular campaign (mailing). The LR model contains 2 independent variables: X1 spend per year in 1000's of dollars (so $2000 will be coded as X1 2) and X2= does customer possess a loyalty card (X2 1 means customer has loyalty card, X2 = 0 means customer does not have the card). Once the model is fitted, the LR coefficients are provided below: = Constant term (BETAO): - 3.5 (negative 3.5) X1 coeff. (BETA1): 0.6 X2 coeff.(BETA2): 1.5 What is the probability that a customer who spends $6000/year and who does NOT have a loyalty card will respond to the campaign? = O About 53% O About 15% About 33% O About 45%
Consider a random process X(t) = A cos o t where a' is a constant and A is a random variable uniformly distributed over (0, 1). Find the auto correlation and covariance of X(t).
(b) (i) Briefly explain how moment generating function of a random variable, y may be used to Generate its moments. (ii) Let the random variable, y have probability density function S(t) = kye-1/2y y20 , elsewhere Where k> 0 is a constant. Find the moment generating function of y and use it to evaluate the mean and variance of y leaving your results in terms of k.
Suppose that we want to build a model that predicts the group membership of a hurricane, either tropical (0) or non-tropical (1) based on the latitude of formation of the huricane. The response variable is the binary variable Type.new (type of hurricane) and the predictor variable is FirstLat (First Latitude). Using R, we build a model by applying the glm () function. For the logistic regression model, we specify family = "binomial". The data is available at https://userpage.fu-berlin.de/soga/200/2010 data sets hurricanes.xlsx. The R code is #set up filename my.filename 1z|) <2e-16 *** 0.96148 -9.446 0.37283 0.03947 9.447 <2e-16 *** --- *# Signif. codes: 0 '*** 0.001 **' 0.01 '*' 0.05'.' 0.1 '' 1 # (Dispersion parameter for binomial family taken to be 1) Null deviance: 463.11 on 336 degrees of freedom *# Residual deviance: 232.03 on 335 degrees of freedom *# AIC: 236.03 *# Number of Fisher Scoring iterations: 6 What is the interpretation of the p-value of the predictor variable…
(b) Let X1, X2, ...,X, be a random sample from the pdf Be z for z 2 0 f(z,0) = 0, otherwise (1) Show that the statistic T(X1, X2, . . , Xn) = X, is complete sufficient for 8. %3D i=1
7
A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.
Chlorophylls a and b are plant pigments that absorb sunlight and transfer the energy into photosynthesis of carbohydrates from CO2 and H2O, releasing O2 in the process. Chlorophylls were extracted from chopped up grass and measured by spectrophotometry. The table shows results for chlorophyll a for four separate analysis of five blades of grass. Chlorophyll a (g/L) Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 1.09 1.26 1.1 1.23 0.85 0.86 0.96 1.21 1.3 0.65 0.93 0.8 1.27 0.97 0.86 0.99 0.73 1.12 0.97 1.03 Four replicate measurements for each blade of grass tell us the precision of the analytical procedure (sanalysis). Differences between mean values for each of the five blades of grass are a measure of variation due to sampling (ssampling). Using Excel and it’s ANOVA function, find the standard deviations attributable to sampling and to analysis, as well as the overall standard deviation arising from both sources.
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The partial differential equation (PDE) by eliminating the arbitrary function f from: z = = xy + f(x² + y²) is_ py+qx8 = y + x² O py+qx = y² + x² py-qxy + x² py+qx=y7x7 O pys+qx8= y² - x²
6. In a large manufacturing company every item produced is inspected for defects and will go through a repair process if there are serious defects. Management wanted to investigate whether items produced on Mondays are more likely to require repairing than items produced on the midweek day Wednesday. A random sample of 9 weeks from the past 5 years was taken and the number of items which required repairing for the 9 weeks are shown in the table below. More Repairing Signed Rank of on Monday Week Monday Wednesday Difference |Difference| A 17 18 -1 NO -1 B 14 17 -3 NO -2 C 19 12 7 YES 6. D 21 17 4 YES 3 E 18 13 YES F 19 10 9 YES G 24 4 20 YES H 25 17 8 YES I 22 16 6 YES (a) A boxplot of the differences in number of items which required repairing on Monday and Wednesday for the 9 sampled weeks is shown below. 米 ++ +++ 十十+ ++ -4 -2 2 4 8. 10 12 14 16 18 20 Differences

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4 random process X (t) has an auto correlation function Rxx (t) = A² + B.e-l, where A and B are positive constants. Find the mean value of the response of a system having an impulse response h (f) = e-kt for t > 0 = 0 for t< 0 %3D where K is a real positive constant, for which X (t) is its input.