Question

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).

Answer #1

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...

A coin is tossed 5 times. Let the random variable ? be the
difference between the number of heads and the number of tails in
the 5 tosses of a coin. Assume ?[heads] = ?.
Find the range of ?, i.e., ??.
Let ? be the number of heads in the 5 tosses, what is the
relationship between ? and ?, i.e., express ? as a function of
??
Find the pmf of ?.
Find ?[?].
Find VAR[?].

(a) A fair coin is tossed five times. Let E be the event that an
odd number of tails occurs, and let F be the event that the first
toss is tails. Are E and F independent?
(b) A fair coin is tossed twice. Let E be the event that the
first toss is heads, let F be the event that the second toss is
tails, and let G be the event that the tosses result in exactly one
heads...

NOTE:KINDLY SOLVE PARTS D AND E.
A fair coin is tossed four times, and the random variable X is
the number of heads in the first three tosses and the random
variable Y is the number of heads in the last three tosses.
a) What is the joint probability mass function of X and Y ?
b) What are the marginal probability mass functions of X and Y
?
c) Are the random variables X and Y independent?
d) What...

A coin is tossed repeatedly until heads has occurred twice or
tails has occurred twice, whichever comes first. Let X be the
number of times the coin is tossed.
Find: a. E(X). b. Var(X).
The answers are 2.5 and 0.25

Let X be the number of heads in three tosses of a fair coin.
a. Find the probability distribution of Y = |X − 1|
b. Find the Expected Value of Y

A coin is tossed 4 times. Let X be the number of times the coin
lands heads side up in those 4 tosses.
Give all the value(s) of the random variable, X. List them
separated commas if there is more than one.
X =

A balanced coin is tossed 3 times, and among the 3 coin tosses,
X heads show. Then the same balanced coin is tossed X additional
times, and among these X coin tosses, Y heads show.
a. Find the distribution for Y .
b. Find the expected value of Y .
c. Find the variance of Y .
d. Find the standard deviation of Y

A balanced coin is tossed 3 times, and among the 3 coin tosses,
X heads show. Then the same balanced coin is tossed X additional
times, and among these X coin tosses, Y heads show.
a. Find the distribution for Y .
b. Find the expected value of Y .
c. Find the variance of Y .
d. Find the standard deviation of Y

A fair coin is tossed three times and the RV X equals
the total number of heads. Find and sketch the pdf,
fX (x), and the PDF
FX (x).

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