Question

One hundred draws are made at random with replacement from the box: [1,1,2,3]
The draws come out as follows: 45 1’s, 23 2’s, and 32 3’s.

1. the standard deviation of the sum of the draws is:

2. the standard deviation for the number of 1’s is:

Answer 1

Console Terminal x-c(rep(1,45),rep(2,23) , rep(3, 32)) [33] 1 1111111 11111222 222222 2 2222 222 2 2 [65] 2 2223 3333 333 3 3 3 3 3333 33 3 3 3 3 3333 3 3 [97] 3 3 3 3 table (x) 45 23 32 [1] 0.8721852 > #std deviation for 1's : to calculate we need to find prob of 1's p-0.45 sd(x) #1. The std deviation of sum of the draws is 0.8722 as shown above #i .e. p=0 . 45 and q- 1-p=0 .55 hence sd = sqrt(p*q/n) [1] 0.55 sqrt (p*q/100) #gives us std deviation of 1's [1] 0.04974937 > #so we can say that 0.04975 is the std deviation of 1's

Above question solved in R.

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