Question

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).

Answer #1

a. Roll a dice, X=the number obtained. Calculate E(X), Var(X).
Use two expressions to calculate variance.
b. Two fair dice are tossed, and the face on each die is
observed. Y=sum of the numbers obtained in 2 rolls of a dice.
Calculate E(Y), Var(Y).
c. Roll the dice 3 times, Z=sum of the numbers obtained in 3
rolls of a dice. Calculate E(Z), Var(Z) from the result of part a
and b.

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)

Three dice are rolled and two fair coins are tossed. Let X be
the sum of the number of spots that show on the top faces of the
dice and the number of coins that land heads up. The expected value
of X is ____?

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

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 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)?

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 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...

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 )....

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