MATH 1280 Assignment Unit 6- University of the People
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Course
MATH 1280
Institution
MATH 1280
MATH 1280 Assignment Unit 6- University of the PeopleMATH 1280 Assignment Unit 6- University of the PeopleMATH 1280 Assignment Unit 6- University of the PeopleMATH 1280 Assignment Unit 6- University of the PeopleMATH 1280 Assignment Unit 6- University of the PeopleMATH 1280 Assignment Unit 6- Unive...
,The size refers to how many times the experiment is done.
The prob refers to the probability of the specific event occurring.
The lower.tail is set to true by default, which means by default it will show the probability below the
specified value.
The log.p is set to false by default, which means probabilities are shown as log of the given input.
2) You can use the dbinom() command (function) in R to determine the probability of getting 0 heads
when you flip a fair coin four times (the probability of getting heads is 0.5):
dbinom(0, size=4, prob=0.5)
Find the equivalent values for getting 1, 2, 3, or 4 heads when you flip the coin four times. TIP: after
you run the first dbinom() command, press the up arrow and make a small change and run it again.
probability of getting exactly 1 head:
> dbinom(1, size=4, prob=0.5)
[1] 0.25
probability of getting exactly 2 heads:
> dbinom(2, size=4, prob=0.5)
[1] 0.375
probability of getting exactly 3 heads:
> dbinom(3, size=4, prob=0.5)
[1] 0.25
probability of getting exactly 4 heads:
> dbinom(4, size=4, prob=0.5)
[1] 0.0625
,3) Use the pbinom() function in R to show the cumulative probability of getting 0, 1, 2, 3, or 4 heads
when you flip the coin 4 times (this is the same as finding the probability than the value is less than or
equal to 0, 1, 2, 3, or 4.)
probability of getting no more than 0 heads:
> pbinom(0, size=4, prob=0.5)
[1] 0.0625
probability of getting no more than 1 head:
> pbinom(1, size=4, prob=0.5)
[1] 0.3125
probability of getting no more than 2 heads:
> pbinom(2, size=4, prob=0.5)
[1] 0.6875
probability of getting no more than 3 heads:
> pbinom(3, size=4, prob=0.5)
[1] 0.9375
probability of getting no more than 4 heads:
>pbinom(4, size=4, prob=0.5)
[1] 1
4) The following R command will show the probability of exactly 6 successes in an experiment that has
10 trials in which the probability of success for each trial is 0.5:
dbinom(6, size=10, prob=0.5)
True
, 5) Read Yakir (2011, pp. 68-69) carefully to review the meaning of the pbinom function (related to
tests that a value will be “equal to” versus “less than or equal to” a criterion value). What is the
probability of getting fewer than 2 heads when you flip a fair coin 3 times (round to 2 decimal places) ?
> pbinom(1, size=3, prob=0.5)
[1] 0.5
6) What is the probability of getting no more than 3 heads when you flip a fair coin 5 times (be sure to
understand the wording differences between this question and the previous one—round to 2 decimal
places)?
> pbinom(3, size=5, prob=0.5)
[1] 0.8125 (or 0.81 when rounded to 2 decimal places)
7) What is the expectation for the time interval between customers entering the store? Be sure to
specify the units of measurement in your answer (see Yakir, 2011, pp. 79-80). Round to 3 decimal
places:
The equation that calculates the expectation for an exponential distribution is 1/lambda, which means
the expectation in this case is 0.25 minutes or 15 seconds.
8) What is the variance of the time interval? Be sure to specify the units of measurement in your
answer. Round to 3 decimal places:
The variance is calculated by 1/(lambda^2). Hence, 1/(4^2) is 0.063 minutes or 3.75 seconds.
9) The pexp() function is introduced at the bottom of Yakir, 2011, p. 79, and there are some tips above.
What is the probability that the time interval between customers entering the store will be less than
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