Question
Asked Sep 10, 2019

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed.

The four numbers that have the largest possible standard deviation are 0, 0, 10 and _______.

(Give your answer as a whole number.)

check_circleExpert Solution
Step 1

To determine the number x from {0,1,2,...,10] such that the standard deviation of 0,0,10 and x is the largest

Step 2

We need to find the value of x which maximizes the expression in x  shown above,

Let X denote the random var iable
taking values 0,0,10, x
f(x)(s tan dard deviation) of 0,0,10, x
E(X)-E(X(E expectation
100x (10 x)
4
16
3x2 -20x300
16
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Let X denote the random var iable taking values 0,0,10, x f(x)(s tan dard deviation) of 0,0,10, x E(X)-E(X(E expectation 100x (10 x) 4 16 3x2 -20x300 16

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Step 3

Method 1: the derivative of the numerator is 6x-20, so the function inc...

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