Test Index

Probability

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Question : 65 of 127

Marks: +1, -0

If two random variables

x

and yare related as

y

=-3 x+4

and standard deviation of

x

2,

then the standard deviation of

y

is related

$-6$
6
18
$3.50$

Solution:

Concept:

Standard deviation is affected only by scaling (multiplication by a constant) and not by shift (addition of a constant).

Explanation:

Given

y = -3x + 4

.

The constant

+4

does not change the standard deviation.

The factor

-3

multiplies the standard deviation by

| -3 | = 3

.

Thus,

\sigma_y = 3 \times \sigma_x = 3 \times 2 = 6

.

Answer:

6

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