An experiment is to flip a coin until a head appears for the
first time. Assume the coin may be biased, i.e., assume that the
probability the coin turns up heads on a flip is a constant p (0
< p < 1). Let X be the random variable that counts the number
of flips needed to see the first head.
(a) Let k ≥ 1 be an integer. Compute the probability mass
function (pmf) p(k) = P(X = k)....
As a binomial question: Flip a coin twice. The probability of
observing a head is 50%, what is the probability that I observe 1
head? binompdf (n, p, x) so binompdf( 2, .50,1) Sampling Proportion
question (8.2): There is a 50% of observing a head. If we flip the
coin 100 times, what is that at most 30% of the flips will be
heads? n*p*(1-p) =100*.50*.50=25 (Do not use my coin example. Use
your own scenario). pˆ=.30 po or μ=50...
I flip a fair coin and recorded the result. If it is head, I
then roll a 6-sided die: otherwise, I roll a 4-sided die and record
the results. Let event A be the die has a 3 or greater. let event B
be I flip tails. (a)-List all the outcomes in the Sample space (b)-
List the outcomes in Event A and B (c)- List the outcomes in A or
not B (d)- Calculate the probability of event A...
Your unfair coin comes up heads with probability 0.6. You flip
it until you get four heads in a row. Let
t be the expected number of times you
flip. Write an equation for t. (Your
equation, if solved, should give the value of
t).
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...
Suppose that you flip a coin 11 times. What is the probability
that you achieve at least 4 tails?
A sign on the pumps at a gas station encourages customers to
have their oil checked, and claims that one out of 5 cars needs to
have oil added. If this is true, what is the probability of each of
the following:
A. One out of the next four cars needs oil.
Probability =
B. Two out of the next eight...
A perfectly balanced coin is tossed, there is equal chance to
get a head (H) or a tail (T ). Consider a random experiment of
throwing SEVEN perfectly balanced and identical coins. Let S denote
the sample space.
a) List the elements in S.
(b) Find the probability that there is three tails and four
heads.
You flip a coin, if it is heads you will have a good day and if
it is tails you will have a bad day. There are 30 days in
total.
(a) What is the expectation and variance of the number of times
you will have a good day throughout this 30 day stretch?
(b) What is the probability that every day will be bad for all
of the 30 days?
If you flip a fair coin, the probability that the result is
heads will be 0.50. A given coin is tested for fairness using a
hypothesis test of H0:p=0.50 versus HA:p≠0.50. The given coin is
flipped 180 times, and comes up heads 110 times. Assume this can be
treated as a Simple Random Sample. The test statistic for this
sample z and the p value