Assume we flip a fair coin 100 times. Use the normal
approximation to the binomial distribution...
Assume we flip a fair coin 100 times. Use the normal
approximation to the binomial distribution to approximate the
probability of getting more than 60 heads.
A fair coin is tossed 400 times.
(a) Using the normal approximation to estimate the chance of
getting exact 200 heads.
(b) To use binomial formula to find the chance of getting exact
200 heads.
Flip a fair coin 100 times. Let X equal the number of heads in
the first 65 flips. Let Y equal the number of heads in the
remaining 35 flips.
(a) Find PX (x) and PY (y).
(b) In a couple of sentences, explain whether X and Y are or are
not independent?
(c) Find PX,Y (x, y).
We flip a fair coin 20 times. Find the probability that we
obtain between 8 and 17 heads, inclusively. Show work and please
explain to someone that hardly understands statistics!
If a symmetric coin is tossed 100 times, by using normal
approximation find the probability that:
a. it comes up H more than 60 times
b. the number of H(X) is between 60 and 90 (60≤X≤90)
1. A) If you flip an unfair coin 100 times, and the probability
for a coin to be heads is 0.4, then the number of heads you expect
on average is:
B) If you flip an unfair coin 100 times, and the probability for
a coin to be heads is 0.4, then the standard deviation for the
number of heads is:
C) If you flip an unfair coin 2 times, and the probability for a
coin to be heads is...
A coin is tossed 279 times. Use either a Normal or Poisson
approximation to approximate the probability that there are at most
43 heads. Show that the approximation is applicable and use the
Padé approximation to determine the result.
DO NOT USE!!!! TI-83, TI-84, TI-89 NOR Excel commands for the
Binomial distribution to determine the result.
Flip a fair coin 4 times. Let ? and ? denote the number of heads
and tails correspondingly.
(a) What is the distribution of ?? What is the distribution of ?
?
(b) Find the joint PMF. Are ? and ? independent?
(c) Calculate ?(? ?) and ?(X≠?)(d) Calculate C??(?, ? ) and
C???(?, ? )
Using R-studio
2. Consider an experiment where we flip a fair coin six
times in a row, and i is the number of heads tossed:
a. Calculate the
probability mass function for i = 0. . . 6 using the equation from
Ross section 2.8 for Binomial Random Variables
b. Conduct a
simulation of this experiment in R, with T trials of the experiment
– pick several values of T from 10 to 10,000.
c. Create a...
A binomial distribution has p = 0.27 and n = 94
Use the normal approximation to the binomial distribution to
answer parts (a) through (d) below.
a) What are the mean and standard deviation for this
distribution?
b) What is the probability of exactly 18 successes?
c) What is the probability of 20 to 27 successes?
d) What is the probability of 13 to 22 successes?