please show detailed working out The formula for calculating

please show detailed working out

The formula for calculating the size (number of bytes) of a WAVE file (used in music) is, size in bytes = sample ratexbit ratex - x number of channelsxnumber of seconds where, sample rate is measured in samples/second bit rate is measured in bits/sample (8 bits = 1 byte) a bit is either a 0 or a 1 number of channels is usually 2 (for a stereo recording) Maree has recorded a 4:13 song with her band, in stereo, at a sample rate of 48000 and a bit rate of 24. She is about the send the WAVE file over to Finland via the internet to be professionally mastered. The song is sent over byte-by-byte. Bits sent over the internet are subject to \"bit flips\" whereby a 1 maybe turn to 0 and a 0 may turn to a 1. The probability of a bit flip occurring is 0.05 for each bit, independent of other bits. If more than 2 bits in a byte have been flipped, the byte is said to be corrupt. What is the probability that a randomly chosen byte is corrupt? Using your result for part (a), estimate the probability that at least 423000 bytes in the song are corrupt.

Solution

Prob for a randomly chosen byte is corrupt is

Prob for > 2bits have been flipped

P(X>2) = 1-P(x=0,1,2)out of 24 bits

= Binomial prob for x>2 when p = 0.05 and n =8

=000579

---------------------------------------------------------------------------------------------------------------------------------

b) Here x >=423000 bytes

Total bytes = 48000x24 = 1152000

p = 0.00579

We can approxiate to Poisson that mean = 1152000x0.00579 =6670.08