An experiment is conducted to study the effect of a power su

An experiment is conducted to study the effect of a power surge on data stored in a digital computed A \"word\" is a sequence of 8 bits. Each hi, is either \"on\" (activated) or \"off\" (not activated) at any given time. Twenty 8-bit words are stored, and a power surge induced. Let, X denote the number of bit reversals that result per word. Assume that X is binomially distributed with n = 8 and p the probability of a bit reversal, unknown. These data result: Find an unbiased estimate for p. Based on the estimate for p just found, approximate the probability that in another P-bit word a similar power surge will result in no bit reversals. A data line utilizes 64 bits. Based on the estimate for p just found, approximate the probability that at most one bit reversal will occur.

Solution

a) unbiased estimate of p is Xbar/n     n=8

now Xbar=(1+0+0+0+0+0+1+1+0+1+2+1+1+0+1+0+2+2+3+0)/20=0.8

so unbiased estimate of p is 0.8/8=0.1 [answer]

b)now we need to find P[X=0] where X~Bin(8,0.1)

P[X=0]=⁸C₀0.1⁰0.9⁸=0.43046721 [answer]

c) let Y be the random variable denoting the number of bit reversals that result per data line

Y~Bin(64,0.1)

we need to find P[Y<=1]=0.0095631 [answer]