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.

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.
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
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 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.