Write the law of multiplication of probability for two indepedent events $A$ and $B$ in a sample space.
Answer
If $A$ and $B$ are the any two events of a finite sample space $U$ i.e. $(P / A)=$ $P ( A )$ and $P ( B / A )= P ( B )$ for two independent events law of multiplication of probability is written as under : $P ( A \cap B )= P ( A ) \times P ( B )$.
The correlation co-efficient between $X$ and $Y$ is $0.4 .$ What will be the value of correlation co-efficient if $5$ is added in each observation of $X$ and $10$ is multipied to each observation $Y\ ?$
Answer
The correlation co-efficient between $X$ and $Y$ will be $0.4$ because correlation coefficient does not change by the change of origin.