Statistics

A random variable X has the distribution law as given below: The variance of the distribution is

If $\overline{X_1}$ and $\overline{X_2}$ are the means of two distributions such that $\overline{X_1} < \overline{X_2}$ and $\overline{X}$ is the mean of the combined distribution, then

The mean deviation from the mean of the AP a, a + d, a + 2d, ..., a + 2nd, is:

In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on it was found that the two scores 43 and 35 were misread as 34 and 53, respectively. The corrected mean of scores is:

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ....., 1 + 100d from their mean is 255, then the value of d is

Let $X_i, i = 1,2,.. , n$ be n observations and $w_i = px_i +k, i = 1,2, ,n$ where p and k are constants. If the mean of $x_i 's$ is 48 and the standard deviation is 12, whereas the mean of $w_i 's$ is 55 and the standard deviation is 15, then the value of p and k should be