Question

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

Answer #1

let x and y be
the random variables that count the number of heads and the number
of tails that come up when two fair coins are flipped. Show that X
and Y are not independent.

I toss 3 fair coins, and then re-toss all the ones that come up
tails. Let X denote the number of coins that come up heads on the
first toss, and let Y denote the number of re-tossed coins that
come up heads on the second toss. (Hence 0 ≤ X ≤ 3 and 0 ≤ Y ≤ 3 −
X.)
(a) Determine the joint pmf of X and Y , and use it to calculate
E(X + Y )....

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)?

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

Suppose Brian flips three fair coins, and let X be the number of
heads showing. Suppose Maria flips five fair coins, and let Y be
the number of heads showing. Let
Z = (X − Y) Compute P( Z = z)
.

Let X represent the difference between number of heads and the
number of tails obtained when a fair coin is tossed 3 times.
a)Find P(X-1)
b)Find E(X)
c)Find Var(X)

Let X be the number showing when one true dice is thrown. Let Y
be the number of heads obtained when (2 ×X) true coins are then
tossed. Calculate E(Y) and Var(Y).

Find the correlation p(X,Y), where X is the number of heads and
Y is the number of tails, if a biased coin is thrown with heads p
and tossed n time?

let X be the
random variable that equals the number of tails minus the number of
heads when n biased coins are flipped (probability for head is
2/3). What is the expected value of X? what is the variance of
X?

Let X represent the difference between the number of heads and
the number of tails when a coin is tossed 42 times. Then P(X=12)=
?
Please show work with arithmetic.

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