In this problem, we study a simple noisy communication channel. suppose that x is a binary signal that takes value −1 and 1 with equal probability. this signal x is sent through a noisy communication channel, and the medium of transmission adds an independent noise term. more precisely, the received signal is y=x+n, where n is standard normal, indpendendent of x. the decoder receives the value y of y, and decides whether x was 1 or −1, using the following decoding rule: it decides in favor of 1 if and only ifp(x=1|y=y)> 2p(x=−1|y=y) it turns out that the decoding rule can be expressed in the form: decide in favor of 1 if and only if y> t, for some threshold t. find the threshhold t. as an intermediate step, find p1≜p(x=1|y=y).p1=now find t. t=

figure c

step-by-step explanation:

hope this .

the number 100 represents the number of trials in the experiment.

49/100 represents the experimental probability of the coin landing heads up.

step-by-step explanation:

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week