Question

Suppose that your boss instead asks that you toss a fair coin six times, record the number of heads, and then repeat the process, for 2000 times in total. How might you simulate this process with a U(0,1) random number generator? Try to generate the outcome for each group of six tosses at once (i.e., use 2000 random numbers, rather than 12,000 individuals outcomes which you bundle into groups of size six).

Answer #1

Let, X denotes number of heads in 6 tosses of fair coin

We have to repeat this process 2000 times. We want such 2000 values of x using U(0,1) variable

First, select 2000 uniform(0,1) variates, let they are, y=(y1,y2, .................,y1999,y2000)

Now, treat them as the probabilities, now we will get values of binomail variable X(i) such that probability of X(i) is yi where X(i) is number of heads in 6 tosses of fair coin at i'th process

Here is the R code for same

y=runif(2000,0,1) # It gives 2000 random values between 0 and
1

X=qbinom(y,6,0.5) # It gives 2000 values of X, where X is defined
above, here in binomail random variable, n=6, p = 0.5 and X is the
assumed value whose probability is y

Suppose you toss a fair coin three times. Which of the following
events are independent? Give mathematical justification for your
answer.
A=
{“heads on first toss”}; B=
{“an odd number of heads”}.
A=
{“no tails in the first two tosses”}; B=
{“no heads in the second and third
toss”}.

Suppose you toss a fair coin 10,000 times. Should you expect to
get exactly 5000 heads? Why or why not? What does the law of
large numbers tell you about the results you are likely to get?
Choose the correct answer below.
1)Should you expect to get exactly 5000 heads? Why or why
not?
A)You shouldn't expect to get exactly 5000 heads, because you
cannot predict precisely how many heads will occur.
B.You shouldn't expect to get exactly 5000 heads,...

You toss a fair coin six times. What is the probability that at
least one toss results in a tail appearing? Round your answer to
four decimal places.

Suppose you toss a coin 100 times. Should you expect to get exactly
50 heads? Why or why not?
A. Yes, because the number of tosses is even, so if the coin
is fair, half of the results should be heads.
B. No, because the chance of heads or tails is the same, the
chance of any number of heads is the same.
C. No, there will be small deviations by chance, but if the
coin is fair, the result...

Language: Python
Write a program to simulate an experiment of tossing a fair coin
16 times and counting the number of heads. Repeat this experiment
10**5 times to obtain the number of heads for every 16 tosses; save
the number of heads in a vector of size 10**5 (call it
headCounts).
You should be able to do this in 1-3 lines of numpy code. (Use
np.random.uniform1 to generate a 2d array of 10**5 x 16 random
numbers between 0 and...

Suppose you are asked to toss a coin 16 times and
calculate the proportion of the tosses that were heads.
a. What shape would you expect this histogram to
be and why?
b. Where you do expect the histogram to be
centered?
c. How much variability would you expect among
these proportions?
d. Explain why a Normal model should not be used
here.

5. If you toss a coin 10 times, you got 8 head out of
ten tosses. What is the probability of this event if the coin is
fair (P[X=8|Coin=normal], X is a random variable representing
number of head out of ten tosses)? What is the probability of this
event if the coin is fake( P[X=8|Coin=fake])?

To test the hypothesis that a coin is fair, you toss it 100
times. Your decision
rules allow you to accept the hypothesis only if you get between 40
and 60 tails in
100 tosses. What is the probability of committing Type II error
when the actual
probability of tails is 0.7?

java
beginner level
NO ARRAYS in program
Flip a coin (Assignment)
How many times in a row can you flip a coin and gets heads?
Use the random number generator to simulate the flipping of the
coin. 0 means heads, 1 means tails.
Start a loop,
flip it, if heads, count it and keep flipping.
If tails, stop the loop.
Display the number of times in a row that heads came up.
Once this is working, wrap a while loop...

Suppose we toss a fair coin n = 1 million times and write down
the outcomes: it gives a Heads-and-Tails-sequence of length n. Then
we call an integer i unique, if the i, i + 1, i + 2, i + 3, . . . ,
i + 18th elements of the sequence are all Heads. That is, we have a
block of 19 consecutive Heads starting with the ith element of the
sequence. Let Y denote the number of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 23 minutes ago

asked 26 minutes ago

asked 31 minutes ago

asked 37 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago