Question

Three fair coins are tossed. Let x equal be the number of heads observed. give the probability distribution for x, and find the mean.

Answer #1

**The
probability distribution for x**

Number of heads | 0 | 1 | 2 | 3 |

possible outcomes | (T,T,T) | (H,T,T),(T,H,T),(T,T,H) | (H,H,T),(T,H,H),(H,T,H) | (H,H,H) |

Probability |

Mean

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 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)?

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)
.

Toss three fair coins and let x equal the number of tails
observed.
a. Identify the sample points associated with this experiment,
and assign a value of x to each sample point. Then list all the
possible values of x.
b. Calculate p(x) for the values x=1 and x=2.
c. Construct a probability histogram for p(x).
d. What is P(x=2 or x=3)?

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 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 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

STATISTICS/PROBABILITY: Let X= the # of heads when 4 coins are
tossed.
a.) Find the expected number of heads
b.) Find the variance and standard deviation
so far I have
x
0
1
2
3
4
P(x)
1/16
4/16
6/16
4/16
1/16

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

Create a probability distribution for tossing four coins. Let X
represent the number of heads.

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