Solution: No, it is not true that for any sets $A$ and $B, P(A) \cup P(B)=P(A \cup B)$ Justification: Let's suppose, $A=\{0,1\}$ And, $B=\{1,2\}$ $\therefore \text{ }A~\cup ~B~=\text{ }\left\{...
We are given, The total number of observations, $n = 100$. Incorrect mean, $\overline x = 20$. And, Incorrect standard deviation, $\sigma = 3$. So, Mean is given by, $\overline {\text{X}} =...
We are given, The mean and standard deviation of Mathematics are $42$and $12$ respectively. The mean and standard deviation of Physics are $32$ and $15$ respectively. The mean and standard deviation...
(i) When the wrong item is omitted, We are given, The number of observations, $n = 20$. The mean before rechecking $ = 10$. The standard deviation before rechecking $ = 2$. Mean is given by,...
We are given $n$ observations ${x_1}$, ${x_2}$, …., ${x_n}$ . Mean of $n$ observations $ = \overline x $. Variance of $n$ observations $ = {\sigma ^2}$. Also, we have variance, $\sigma = \sqrt...
We are given that, The mean of six observations $ = 8$. The standard deviation of six observations $ = 4$. Let us consider the six observations as ${x_1}$, ${x_2}$, ${x_3}$, ${x_4}$, ${x_5}$ and...
We are given, the mean and variance of eight observations are $8$ and $16$ respectively. Also, we have five observations $2$, $4$, $10$, $12$ and $14$. Suppose that the remaining two observations to...
We are given, the mean and variance of eight observations are $9$ and $9.25$ respectively. Also, we have six observations $6$, $7$, $10$, $12$, $12$ and $13$. Suppose that the remaining two...