Conducting a Simulation
For example, say we want to simulate the probability of getting
“heads” exactly...
Conducting a Simulation
For example, say we want to simulate the probability of getting
“heads” exactly 4 times in 10 flips of a fair coin.
One way to generate a flip of the coin is to create a vector in
R with all of the possible outcomes and then randomly select one of
those outcomes. The sample function takes a vector of elements (in
this case heads or tails) and chooses a random sample of size
elements.
coin <- c("heads","tails")...
1. Let n be an odd positive integer. Consider a list of n
consecutive integers.
Show...
1. Let n be an odd positive integer. Consider a list of n
consecutive integers.
Show that the average is the middle number (that is the number
in the
middle of the list when they are arranged in an increasing
order). What
is the average when n is an even positive integer instead?
2.
Let x1,x2,...,xn be a list of numbers, and let ¯ x be the
average of the list.Which of the following
statements must be true? There might...
1
A fair coin is flipped 15 times. Each flip is independent. What
is the probability...
1
A fair coin is flipped 15 times. Each flip is independent. What
is the probability of getting more than ten heads?
Let X = the number of heads in 15 flips of the fair coin. X
takes on the values 0, 1, 2, 3, ..., 15. Since the coin is fair, p
= 0.5 and q = 0.5. The number of trials is n = 15. State the
probability question mathematically.
2
Approximately 70% of statistics students do their...
1.
a.) Suppose you draw 8 cards from a standard deck of 52 cards,
one after...
1.
a.) Suppose you draw 8 cards from a standard deck of 52 cards,
one after the other, without replacement. Find the probability that
the last card is a club given that the first 7 cards are clubs.
b.) An urn contains 6 green, 10 blue, and 17 red balls. You take
3 balls out of the urn, one after the other, without replacement.
Find the probability that the third ball is green given that the
first two balls were...
16) Players A and B take turns drawing from an urn of 10 balls.
One ball...
16) Players A and B take turns drawing from an urn of 10 balls.
One ball contains a prize, and the rest contain nothing. If player
A draws first, and all draws are without replacement, find the
probability of A winning. Is it more or less than the probability
of B winning?
17) 3 fair coins are fipped behind a screen so that you cannot
see the result. What is the probability that there is at least 1
tail? A...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.39. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.04 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
1. A 4-digit number is created from the numbers {1,2,3,4,5,6}.
How many ways can the digits...
1. A 4-digit number is created from the numbers {1,2,3,4,5,6}.
How many ways can the digits be chosen so that the number is more
than 1500?
2. An applied statistics class contains 30% sophomores, 40%
juniors, and the rest seniors. If 40% of the sophomores, 20% of the
juniors, and 10% of the seniors will fail, what is the probability
a randomly selected student in the class will fail?
3. A coin is flipped 10 times or until 3 heads...
Randomly selected students were given five seconds to estimate
the value of a product of numbers...
Randomly selected students were given five seconds to estimate
the value of a product of numbers with the results shown below.
Estimates from students given
1×2×3×4×5×6×7×81×2×3×4×5×6×7×8:
45000, 1000, 500, 1500, 856, 1000, 1252, 200, 1110, 400045000,
1000, 500, 1500, 856, 1000, 1252, 200, 1110, 4000
Estimates from students given
8×7×6×5×4×3×2×18×7×6×5×4×3×2×1:
2000, 2050, 100000, 40320, 300, 10000, 550, 400, 377,
1000002000, 2050, 100000, 40320, 300, 10000, 550, 400, 377,
100000
Use a 0.050.05 significance level to test the claim that the...