An information source generates symbols at random from a four-letter alphabet {a, b, c, d} with probabilities

P r[a] = 1/2,
P r[b] = 1/4,
P r[c] = 1/8,
P r[d] = 1/8.

A coding scheme encodes these symbols into binary codes as follows:

0
10
110
111

Let X be the random variable denoting the length of the code, ie, the number of binary symbols

a. What is the range of X?
b. Sketch the cdfF_X (x) of X and specify the type of X
c. Find P(X≤1),P(X>1)& P(1≤X≤2)

Given that abcd is a parallelogram solve for m

The table represents a linear function. what is the slope of the function? –6 –4 4 6

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)