Suppose a spinner picks a value from 1, 2, 3, 4 each with probability 1/4 and it

Question

Suppose a spinner picks a value from 1, 2, 3, 4 each with probability 1/4 and it is repeatedly spun until each of the numbers 1 through 4 is spun. What is the mean number of spins? Let R be the number of resistors and let C be the number of capacitors, and T be the number of transistors in a circuit board. R has mean 35 and variance 4, C has mean 54 and variance 9, and T has mean 21 and variance 16. Assuming that the numbers of components are independent, find the mean and the standard deviation of the total number of electronic components in a circuit board.

Explanation / Answer

12. E(C+T+R) = E(C) +E(T)+E(R)

= 54+21+35

= 110

V(X+Y+Z) = V(X) + V(Y) + V(Z)

Therefore, V(C+T+R) = V(C) + V(T) + V(R)

= 4+9+16

= 41

The mean and the standard deviation of the total no. of electronic components in a circuit board are 110 and 41 , respectively

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