Probability and Random Processes for Electrical and Computer by John A. Gubner

By John A. Gubner

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Extra info for Probability and Random Processes for Electrical and Computer Engineers, 1st Edition

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For any subset A ⊂ Ω, put P(A) := ∑ p(ω ). ω ∈A In particular, to model equally likely outcomes, or equivalently, outcomes that occur “at random,” we take p(ω ) = 1/M. In this case, P(A) reduces to |A|/|Ω|. 12. A single card is drawn at random from a well-shuffled deck of playing cards. Find the probability of drawing an ace. Also find the probability of drawing a face card. 20 Introduction to probability Solution. The first step in the solution is to specify the sample space Ω and the probability P.

Since balls are chosen at random, the desired probability is number of ways to choose five green balls and seven red balls . number of ways to choose 12 balls In the numerator, the five green balls must be chosen from the 11 available green balls, and the seven red balls must be chosen from the nine available red balls. In the denominator, the total of 5 + 7 = 12 balls must be chosen from the 11 + 9 = 20 available balls. 132. 41. Consider a collection of N items, of which d are defective (and N − d work properly).

K0 ! (n − k0 )! n k0 becomes the binomial coefficient. Unordered sampling with replacement Before stating the problem, we begin with a simple example to illustrate the concepts involved. 46. An automated snack machine dispenses apples, bananas, and carrots. For a fixed price, the customer gets five items from among the three possible choices. For example, a customer could choose one apple, two bananas, and two carrots. To record the customer’s choices electronically, 7-bit sequences are used. For example, the sequence (0, 1, 0, 0, 1, 0, 0) means one apple, two bananas, and two carrots.

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