Back to STATISTICS

JEE MATHEMATICS MCQ: STATISTICS

1 Hard

1 of 1

Application +4 | -1

If

Z = aX + bY

and

r

be the correlation coefficient between

X\;and\;Y

, then

\sigma _Z^2

is equal to

View answer and explanation

Correct option: A

{a^2}\sigma _X^2 + {b^2}\sigma _Y^2 + 2abr{\sigma _X}{\sigma _Y}

The correct answer is A (

{a^2}\sigma _X^2 + {b^2}\sigma _Y^2 + 2abr{\sigma _X}{\sigma _Y}

) because it represents the variance of a linear combination of two random variables, considering their correlation.

More Questions from STATISTICS

Practice All Chapter MCQs →

If the mean of a set of observations

{x_1},{x_2}, \ldots ,{x_n}

\bar X,

then the mean of the observations

{x_i} + 2\;i;i = 1,\;2, \ldots ,n

is The sum of 10 items is 12 and sum of their squares is 18 , then standard deviation will be In a family, there are 8 men, 7 women and 5 children whose mean ages separately are respectively 24,20 and 6 years. The mean age of the family is The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is

1,3,5, x, y

are 5 observations. Mean of these observations is 5 and variance is 8. Sum of the cubes of the two missing number equals: If s.d. of a set of observations is 8 and if each observation is divided by

-2,

the s.d. of the new set of observations will be