Question

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

Answer #1

Two tails or two heads cannot be obtained in 0 or 1 tosses.

The sample space for tossing of a coin 2 times is : HH,HT,TH,TT out of which 2 heads or 2 tails occur in HH, TT.

The sample space for tossing of a coin 3 times is : HHH,HHT,HTH,THH,HTT,THT,TTH,TTT out of which 2 heads or 2 tails occur in HTH,THH,HTT,THT.

So, Probability distribution of X:

X | 2 | 3 |

P(X) |

a)

b)

Now

So,

7.- A balanced coin is thrown until heads or 3 tails appears,
whichever comes first. Let X be the number of releases required.
Obtain the probability function of the random variable X to
calculate the expected number of releases. Round the result to two
decimal places.

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).

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Deﬁne (X = number of the toss on
which the ﬁrst H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Deﬁne (X = number of the toss on
which the ﬁrst H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function

(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...

If a quarter is tossed five times and comes up tails twice and
heads three times, the probability of heads on the next two tosses
is ...

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[?].

Consider the experiment of tossing a fair coin until a tail
appears or until the coin has been tossed 4 times, whichever occurs
first. SHOW WORK.
a) Construct a probability distribution table for the number of
tails
b) Using the results in part a make a probability distribution
histogram
c) Using the results in part a what is the average number of
times the coin will be tossed.
d) What is the standard deviation (nearest hundredth) of the
number of...

You flip a coin until getting heads. Let X be the number of coin
flips.
a. What is the probability that you flip the coin at least 8
times?
b. What is the probability that you flip the coin at least 8
times given that the first, third, and fifth flips were all
tails?
c. You flip three coins. Let X be the total number of heads. You
then roll X standard dice. Let Y be the sum of those...

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 31 minutes ago

asked 39 minutes ago

asked 39 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago