Question

**Suppose a coin is tossed three times.**

(a) Using the "c" and "s" labels, list all possible outcomes in the
sample space.

(b) For each result in the sample space, define the random variable
X as the number of faces minus the number of stamps observed. Use
the fact that all the results from part (a) have the same
probability. Find the probability distribution of X.

(c) Use the probability distribution found in (b) to find the mean
and standard deviation of X.

Answer #1

a) All possible outcomes in the sample space={(c,c,c),(c,c,s),(c,s,c),(s,c,c),(s,s,c),(s,c,s),(c,s,s),(s,s,s,)}

b) Given,they have similar probability,so,

X | P(X) |

3 | |

2-1=1 | |

1-2=-1 | |

0-3=-3 |

c)Mean of X=

Standard deviation of X=

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 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 =

Suppose that a fair coin is tossed 10 times.
(a) What is the sample space for this experiment?
(b) What is the probability of at least two heads?
(c) What is the probability that no two consecutive tosses come
up heads?

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 coin is tossed 4 times. the sample space consists of the set
of possible sequences of heads and tails
a) for how many points of the sample space is the number of
heads more than the number of tails
b) for how many points is the number of heads less than the
number of tails
PLEASE GIVE DETAILED ANSWER

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).

A coin is tossed three times. An outcome is represented by a
string of the sort
HTT
(meaning heads on the first toss, followed by two tails).
The
8
outcomes are listed below. Assume that each outcome has the same
probability.
Complete the following. Write your answers as fractions.
(a)Check the outcomes for each of the three events below. Then,
enter the probability of each event.
Outcomes
Probability
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Event A: Exactly two...

1. A fair coin is tossed ten times. (a) What is the probability
that all ten tosses produce the small result? (b) What is the
probability that the results alternate, i,e., Tail is followed by
Head and head is followed by Tail? (c) What is the probability that
the first five tosses produce identical results?
2. A point M is chosen in random within the unit square . (a)
What is the probability that M is closer to Y- axis...

a biased coin tossed four times P(T)=2/3 x is number
of tails observed
construct the table of probabulity function f(x) and cumulative
distributive function F(x)
and the probability that at least on tail is observed ie
P(X>1)

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