1-1.1 A six-cell storage battery having a nominal terminal voltage of 12 Vis connected in series·with an ammeter and a resistor labeled 6 ohms. a) List as many random quantities as you can for this circuit. b) If the battery voltage can have _ any value between 10.5 and 12.5, the resistor can have any value within 5% of its marked value, and the ammeter reads within 2% of the true current, find the range of possible ammeter readings. Neglect ammeter resistance. c) List any nonrandom quantities you can for this circuit. 1-1.2 In determining the probability characteristics of printed English, it is common to consider a 27-letter alphabet in which the space between words is counted as a letter. Punctuation is usually ignored. a) Count the number of times each of the 27 letters appears in this problem. b) On· the basis of this count, deduce the most probable letter, the next most probable letter, and the least probable letter (or letters). 1-2.1 For each of the following random experiments, list all of the possible outcomes and state whether these outcomes are equally likely. a) Flipping two coins. b) Observing the last digit of a telephone number selected at random from the directory. c) Observing the sum of the last two digits of a telephone number selected at random from the directory. 1-2.2 State whether each of the following defined events is an elementary event. a) Obtaining a seven when a pair of dice are rolled. b) Obtaining two heads when three ct>ins are flipped. c) Obtaining an ace when a card is selected at random from a deck of cards. d) Obtaining a two of spades when a card is selected at random from a deck of cards. e) Obtaining a two when a pair of dice are rolled. f ) Obtaining three heads when three coins are flipped. g) Observing a value less than ten when a random voltage is observed. h) Observing the letter e sixteen times in a piece of text.
1-1.1 A six-cell storage battery having a nominal terminal voltage of 12 Vis connected in
series·with an ammeter and a resistor labeled 6 ohms.
a) List as many random quantities as you can for this circuit.
b) If the battery voltage can have _ any value between 10.5 and 12.5, the resistor can
have any value within 5% of its marked value, and the ammeter reads within 2%
of the true current, find the range of possible ammeter readings. Neglect ammeter
resistance.
c) List any nonrandom quantities you can for this circuit.
1-1.2 In determining the
consider a 27-letter alphabet in which the space between words is counted as a letter.
Punctuation is usually ignored.
a) Count the number of times each of the 27 letters appears in this problem.
b) On· the basis of this count, deduce the most probable letter, the next most probable
letter, and the least probable letter (or letters).
1-2.1 For each of the following random experiments, list all of the possible outcomes and
state whether these outcomes are equally likely.
a) Flipping two coins.
b) Observing the last digit of a telephone number selected at random from the directory.
c) Observing the sum of the last two digits of a telephone number selected at random
from the directory.
1-2.2 State whether each of the following defined events is an elementary
a) Obtaining a seven when a pair of dice are rolled.
b) Obtaining two heads when three ct>ins are flipped.
c) Obtaining an ace when a card is selected at random from a deck of cards.
d) Obtaining a two of spades when a card is selected at random from a deck of cards.
e) Obtaining a two when a pair of dice are rolled. f
) Obtaining three heads when three coins are flipped.
g) Observing a value less than ten when a random voltage is observed.
h) Observing the letter e sixteen times in a piece of text.
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