Math/Stats Given: There are 4 independent input variables (x 1, x 2, x 3, x 4) that could influen...
Math/Stats
Given:
There are 4 independent input variables (x 1, x 2, x 3, x 4) that could influence the output sensor reading (y).
Required:
y ~ f(x 1 , x 2, x 3, x 4)
● If we assume f is a linear function of the input variables, propose an approach to determine which input variable (xi) is the dominant factor in the variability of y.
Homework Answers
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Math/Stats Given: There are 4 independent input variables (x 1, x 2, x 3, x 4) that could influen...
stats (6) Consider the following joint probability density function of the random variables X and f(x,y)...
stats
(6) Consider the following joint probability density function of the random variables X and f(x,y) = 9, 1<x<3, 1<y< 2, elsewhere. (a) Find the marginal density functions of X and Y. (b) Are X and Y independent? (c) Find P(X > 2).
2. Let X and Y are independent random variables with the same mass function f(-1) f(1)...
2. Let X and Y are independent random variables with the same mass function f(-1) f(1) = 1/2. Let Z = XY. Show that X, Y, Z are pairwise independent but they are not independent. (Here、X,, . .. , xn are said to be pairwise independent if every pair Xi, X, with i f j are independent.)
Stats please show the steps 10. Suppose we have a frequency function for two variables X...
Stats please show the steps
10. Suppose we have a frequency function for two variables X and Y, f(x,y)= , for x = 0, 1, 2, 3 30 and y = 0, 1, 2. a. Determine the marginal distributions of X and Y. b. Determine E(X) and E(Y). c. Determine E(X+Y). d. If Z= 2X+10, determine E(Z). e. Determine E(XY). f. Determine cov(X,Y). g. Are X and Y independent? Justify your answer.
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8...
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
3
8
4
10
15
(a)
Develop a scatter diagram for these data.
1 2 3 4 5 g 2 N to Go 4 1 2 0 1 3 4 5 6 1 2 3 (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x...
4. Suppose X and Y are independent random variables with the same probability distribution, given by...
4. Suppose X and Y are independent random variables with the same probability distribution, given by the cumulative distribution function if t 2 1 if t < 1 F(t)= 1 -t-3 (a) (10 points) Compute E(X). (b)(10 points) Compute E(XY). Chr
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 5 10 14 (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.
Write a user-defined MATLAB function for the following math function y(x). The input to the function...
Write a user-defined MATLAB function for the following math function y(x). The input to the function is x and the output is y. y(x)=-(0.2*x^4)+((e^-0.5*x)*x^3)+7*x^2 Call the function to calculate y(x) over the interval -3 ≤ x ≤ 4 for each increment of 1. Display x and corresponding y(x) in a text file with labeled column headings. Use the type command to display the contents in the text file.
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3)...
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3) dy where x(t) is the input and y(t) is the output, a) Determine whether the system is linear or non-linear. b) Determine the impulse response h(t, to) of the system by setting x(t)= 8(t–to). c) Determine whether the system is time invariant or time variant. d) Determine whether the system is causal or non-causal.
stats
(6) Consider the following joint probability density function of the random variables X and f(x,y) = 9, 1<x<3, 1<y< 2, elsewhere. (a) Find the marginal density functions of X and Y. (b) Are X and Y independent? (c) Find P(X > 2).
2. Let X and Y are independent random variables with the same mass function f(-1) f(1) = 1/2. Let Z = XY. Show that X, Y, Z are pairwise independent but they are not independent. (Here、X,, . .. , xn are said to be pairwise independent if every pair Xi, X, with i f j are independent.)
Stats please show the steps
10. Suppose we have a frequency function for two variables X and Y, f(x,y)= , for x = 0, 1, 2, 3 30 and y = 0, 1, 2. a. Determine the marginal distributions of X and Y. b. Determine E(X) and E(Y). c. Determine E(X+Y). d. If Z= 2X+10, determine E(Z). e. Determine E(XY). f. Determine cov(X,Y). g. Are X and Y independent? Justify your answer.
Part 2. Random Variables 4. Two independent random variables Xand y are given with their distribution laws 0.3 0.7 0.8 0.2 Pi Find the distribution law and variance for the random variable V-3XY 5. There are 7 white balls and 3 red balls in a box. Balls are taken from the box without return at randomm until one white ball is taken. Construct the distribution law for the number of taken balls. 6. Let X be a continuous random variable...
Given are five observations for two variables, x and
y.
xi
1
2
3
4
5
yi
3
8
4
10
15
(a)
Develop a scatter diagram for these data.
1 2 3 4 5 g 2 N to Go 4 1 2 0 1 3 4 5 6 1 2 3 (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x...
4. Suppose X and Y are independent random variables with the same probability distribution, given by the cumulative distribution function if t 2 1 if t < 1 F(t)= 1 -t-3 (a) (10 points) Compute E(X). (b)(10 points) Compute E(XY). Chr
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3) dy where x(t) is the input and y(t) is the output, a) Determine whether the system is linear or non-linear. b) Determine the impulse response h(t, to) of the system by setting x(t)= 8(t–to). c) Determine whether the system is time invariant or time variant. d) Determine whether the system is causal or non-causal.
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