Question

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)

Answer #1

Possible outcomes are (HHH),(HHT),(HTH),(HTT),(THH),(THT),(TTH),(TTT)

-3 | -1 | 1 | 3 | |

b)

c)

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.

Let X represent the difference between the number of heads and
the number of tails when a coin is tossed 48 times. Then
P(X=8)=
So far I got 0.05946 but it keeps telling me I'm wrong

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).

Let X be the random variable representing the difference between
the number of headsand the number of tails obtained when a fair
coin is tossed 4 times.
a) What are the possible values of X?
b) Compute all the probability distribution of X?
c) Draw the cumulative distribution function F(x) of the random
variable X.

Complete the following:
(a) Var (X) ≥ 0 for any discrete r.v. X. Also, explain why X
is constant if and only if
Var (X) = 0. Hint: write Var (X) = E (X − µ)2 = Px (x − µ)2 pX
(x), where µ = E (X).
(b) Let X represent the dierence between the number of heads
and the number of tails obtained
when a fair coin is tossed n times. Find E (X) and Var
(X)

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 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

A coin is tossed five times. Let X = the number of heads. Find
P(X = 3).

Let X equal the number of flips of a fair coin that are required
to observe tails–heads on consecutive flips. d) Find E(X + 1)^2 (e)
Find Var(kX − k), where k is a constant

Question 2
Tossing a coin 15 times, let be the number of tails
obtained.
(a) The mean of this binomial distribution is .
(b) The standard deviation (to the neatest tenth) of this
binomial distribution is .
(c) The the probability of getting 6 heads is (round
to the nearest thousandth).
(d) The probability of getting at least 2 tails
is (round to 6 decimal places).
(e) The probability that the number of tails is between 5 and
10, exclusive, is (round to the...

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