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# Tricky S1 question... Help! Watch

1. A random variable R takes the integer value r with probability p(r), where:

p(r) = kr^3 r = 1,2,3,4
p(r) = 0 otherwise.

Find

a) the value of k, and display the distribution on graph paper.
b) the mean and the variance of the distribution

a)
r: 1 2 3 4
(R=r) 1k 8k 27k 64k

1k + 8k + 27k + 64k = 1

k( 1 + 8 +27 +64) = 1

Therefore k = 1/100

b) I worked out the mean to be 177/50 (which is correct) and tried to find the variance by trying to find E(R^2):

r : 1 4 9 16
R=r) : 1/100 8/100 27/100 64/100

E(R^2) = (1 x 1/100) + (4 x 8/100) + ( 9 x 27/100) + (16 x 64/100)
= 1300/100 = 650/50

Variance = E (R^2) - Mean
= 650/50 - 177/50
= 473/50 (WRONG!)

The answer I get doesn't match the answer in the book. Help please!
2. (Original post by Mambo No. 5)
Variance = E (R^2) - Mean
= 650/50 - 177/50
= 473/50 (WRONG!)

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The answer I get doesn't match the answer in the book. Help please!
The issue is that . So you've just got the wrong formula for variance.

Try what you did again, but this time square the mean.
3. (Original post by .ACS.)
The issue is that . So you've just got the wrong formula for variance.

Try what you did again, but this time square the mean.
Thank you! Got the right answer. +1rep.

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