Case Study

Case Study $1.$

Given the following data:

Variance of X$=9$

Regression equations:

$4$X$-5$Y$+33=0$

$20$X$-9$Y$-107=0$

Case study $2.$ Given the differential equation dy$/$dx $=($x$-$y$),$ y$(0)=1.$ Answer the following question based on the problem.

Question $1$: Based on case study $1-$ Coefficient of correlation between X and Y is $\_\_\_\_\_\_$

Question $2$: Based on case study $1-$ Mean Value of X is $\_\_\_\_$

Question $3$: Based on case study $1-$ Mean Value of Y is $\_\_\_\_$

Question $4$: Based on case study $1-$ Standard deviation of X is $\_\_\_\_$

Question $5$: Based on case study $1-$ Standard deviation of Y is $\_\_\_\_$

Question $6$: Based on case study $2-$ initial value for x given in the problem is $\_\_\_\_\_\_$

Question $7$: Based on case study $2-$ taking the step size h $=0\mathrm{.}2,$ first approximate value of y at x$=0\mathrm{.}2$ is $\_\_\_\_\_\_\_$

Question $8$: Based on case study $2-$ value of y$(0\mathrm{.}2)$ correct upto $3$ decimal places can be achived in $\_\_\_\_\_\_$ number of approximations.

Question $9$: Based on case study $2-$ value of y$(0\mathrm{.}2)$ correct upto $3$ decimal places is approximately $\_\_\_\_\_\_\_\_\_\_\_$

Question $10$: The process of getting successive approximations in Picard's method stops when desired degree of accuracy till k$^$th decimal place is arrived i$.$e$.$ for two successive approximations $($say$)$ y$^($n$)$ and y$^($n$-1),$ absolute value of y$^($n$-1)-$ y$^($n$)$ is less than or equal to $\_\_\_\_\_\_\_\_\_$