If the following distribution is a probability distribution of variable $X$, then find the constant $C$.$P(x)=C\left(\frac{1}{4}\right)^x, x=1,2,3,4 .$ OR State any four properties of binomial distribution.
The linear equation fitted using the data of $7$ weeks for a variable $y$ is $\hat{y}=25.1 - 1.3t,$ Estimate the value of $y$ for the eighth and ninth week.
Find the value of correlation co-efficient $r$ from the following data and interpret it:$n =10, \sum( x -\overline{ x })( y -\overline{ y })=60, S _{ x }=5, S _{ y }=6$
The wholesale price index number of the year $2015$ and $2016$ are found to be $150.2$ and $165.7$ respectively. Find the rate of inflation using index numbers of both the years.