A simple binary communication channel carries messages by using two signals 0 and 1. It was assumed that for a given binary channel, 40% of the time a 1 is transmitted; the probability that a transmitted 0 is corectly received is 0.90; the probability that lis correctly received 0.95. This information is illustrated in Figure 1 where A= event that 1 is transmitted. A= event that 0 is transmitted. B = event that 1 is received. B = event that 0 is received. A B A Figure 1: A single-stage binary communication channel

Jay-Z has applied to both The School of Hard Knocks and The University of OG's. He thinks the probability that The School of Hard Knocks will admit him is 0.4, the probability that The University of OG's will admit him is 0.5, and the probability that both will admit him is 0.2. Creating a Venn Diagram is Helpful. What is the probability that Jay-Z gets into The School of Hard Knocks but not The University of OGʻs?

When LeBron James shoots a free throw, he hits with a probability of 0.9 and misses with a probability of 0.1. Assume that the result of his previous free throw (whether a hit or a miss), does not affect the probability with which he hits the current throw, i.e., for any free throw he shoots, he hits with a probability of 0.9 and misses with a probability of 0.1. When he hits a free throw, he makes one point and when he misses a free throw, he makes zero points. Answer the following questions with this information. Let P1 denote a random variable that represents the number of points LeBron James makes when he shoots only one free throw. 1. How many possible values can P1 take? Develop a probability distribution for P1 (Very important: Enter the values of P1 in increasing order as you go down in the table) P1 f(P1) (1 decimal) (1 decimal)

A binary communication channel carries data as one of two types of signals denoted by 0 and 1. Owing tonoise, a transmitted 0 is sometimes received as a 1 and a transmitted 1 is sometimes received as a 0. For agiven channel, assume a probability of 0.94 that a transmitted 0 is correctly received as a 0 and a probability0.91 that a transmitted 1 is received as a 1. Further assume a probability of 0.45 of transmitting a 0. If asignal is sent, determine1. Probability that a 1 is received2. Probability that a 0 is received3. Probability that a 1 was transmitted given that a 1 was received4. Probability that a 0 was transmitted given that a 0 was received5. Probability of an error