Question

Let X denote the number of heads than occur when four coins are tossed at random. Under the assumptions that the four coins are independent and the probability of heads on each coin is 1/2,X is B(4,1/2). One hundred repetitions of this experiment results in 0,1,2,3, and 4 heads being observed on 7,18,40,31, and 4 trials, respectively. Do these results support the assumption that the distribution of X is B(4,1/2)?

Answer #1

Three fair coins are tossed. Let x equal be the number of heads
observed. give the probability distribution for x, and find the
mean.

Let p denote the probability that a particular coin will show
heads when randomly tossed. It is not necessarily true that the
coin is a “fair” coin wherein p=1/2. Find the a posteriori
probability density function f(p|TN ) where TN is the observed
number of heads n observed in N tosses of a coin. The a priori
density is p~U[0.2,0.8], i.e., uniform over this interval. Make
some plots of the a posteriori density.

STATISTICS/PROBABILITY: Let X= the # of heads when 4 coins are
tossed.
a.) Find the expected number of heads
b.) Find the variance and standard deviation
so far I have
x
0
1
2
3
4
P(x)
1/16
4/16
6/16
4/16
1/16

let X and Y be
the random variables that count the number of heads and the number
of tails that come up when three fair coins are tossed. Determine
whether X and Y are independent

A fair coin has been tossed four times. Let X be the number of
heads minus the number of tails (out of four tosses). Find the
probability mass function of X. Sketch the graph of the probability
mass function and the distribution function, Find E[X] and
Var(X).

Create a probability distribution for tossing four coins. Let X
represent the number of heads.

Let Y denote the number of “sixes” that occur when two dice are
tossed. (Each of these dice has six sides with one, two, three,
four, five, and six dots respectively. Note that the random
variable is not the number of dots).
(a) When two dice are tossed, how many outcomes are possible?
Write out these outcomes. (Hint: your outcomes should correspond to
the number of 6s since that is the random variable here.)
(b) Derive the probability distribution of...

A fair coin is tossed three times. Let X be the number of heads
among the first two tosses and Y be the number of heads among the
last two tosses. What is the joint probability mass function of X
and Y? What are the marginal probability mass function of X and Y
i.e. p_X (x)and p_Y (y)? Find E(X) and E(Y). What is Cov(X,Y) What
is Corr (X,Y) Are X and Y independent? Explain. Find the
conditional probability mass...

We toss two coins. Let X be the number of heads.
(a) [2 pts] Find the sample space S for X.
(b) [2 pts] Find P(X = 0).
(c) [4 pts] Find the mean of the number of heads.
(d) [4 pts] Find the variance of the number of heads.

Consider a random experiment of throwing FOUR perfectly balanced
and identical coins. Suppose that for each toss that comes up heads
we win $4, but for each toss that comes up tails we lose $3.
Clearly, a quantity of interest in this situation is our total
wining. Let X denote this quantity. Answer the following
questions.
(a) What are the values that the random variable X takes?
(b) Find P(X = 16) =? & P(X = 2) =? & P(X...

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