A source emits independent sequences of symbols from a source alphabet Q4: containing four symbols with probabilities: P(A)= 2P(C) = 0.4,and P(B) = 3P(D). i) Compute the entropy of the source ii) Design a source encoder with a block size of (a) one, and (b) two. (. %3D %3D
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- Suppose the probability of incorrectly transmitting a single bit is . Compute the probability of correctly receiving a -word coded message made up of -bit words.We know that the expected height of trees in a national park is 25 meters, with a standard deviation of 5 meters. By using Markov's inequality, estimate the upper bound for the probability that a tree is equal to or taller than 60 meters. Please round your result to three decimal places.Suppose that the number of accidents occurring on a highway each week is a Poisson random variable with parameter lambda(λ) = 7. a) What is the probability that there there are at least 4 accidents in a week? b) Given that at least one accident occurs in a week, what is the conditional probability that the accident occurs 5 times or less in a week?
- It is known from the past experience that wrong-number calls are received by a switch-board at a Poisson rate of 1 every 2 hours. What is the probability that the operator will receive at least 3 wrong-number calls in an 8-hour workday?Suppose an insect lays a very large number of eggs Y, where Y ~ Po(lambda), and suppose that each egg survives with probability p. Assuming that the egg's survival is independent, on the average, how many eggs will survive?If 90% of the parts produced by a certain machine do notare not defective and which are chosen at random and withdiscount 25 pieces in production, what is the probabilitythat at least 22 of these parts are functional (not defective)? Calculate the expectation and variance of the number ofnon-defective parts.
- a cereal company claims that the mean weight of the cereal in its packets is at least 14oz. express the null hypothesis and the alternatvie hypothesis in symbolic formSuppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?A traffic enforcer counts the number of vehicles at a specific location in the highway. In hiscounting, there are 420 vehicles arrived in span of 1 hour. Assuming that the arrival of vehicles isPoisson distributed, estimate the probabilities of having 7 vehicles arriving over a 30-second timeinterval, over the next one minutes.
- Out of two hundred fifty-six megabytes-memory of the android phone, there is a probability of one error due to bugs every month. If your android phone continues to run for two days with one thousand twenty-four gigabytes of memory, and we intend to have no errors over that two days, what is the probability of having no errors in that two days?A machine has a probability of producing a defective equal to 0.05 every time it produces a product. If three of its products are selected randomly and independently during a shift, what is the probability that a quality engineer will find no defectives in the three?Suppose 10 balls are put into 5 boxes, with the location of the 10 balls being chosen independently of the others, and with each box being equally likely to receive any given ball. Let X denote the number of boxes that do not contain a ball. Find the expectation and variance of X.