PYQs Based Test - 17 : Mean, Mode, Median and Std Deviation

Suppose the probability that a coin toss shows "head" is p, where 0 < p < 1. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is

Consider the two statements.

S₁ : There exist random variables X and Y such that

(E[X - E(X)) (Y - E(Y))])² > Var[X] Var[Y]

S₂ : For all random variables X and Y,

Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]

Which one of the following choices is correct?

A machine produces 0, 1 or 2 defective pieces in a day with an associated probability of $\frac{1}{6}$, $\frac{2}{3}$ and $\frac{1}{6}$ respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

Marks obtained by 100 students in an examination are given in the table.What would be the mean, median, and mode of the marks obtained by the students?

Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list

R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged