Question
In: Statistics and Probability
Begin by creating a probability distribution for the number of heads in five tosses of a...
Begin by creating a probability distribution for the number of
heads in five tosses of a coin. List the different possible
outcomes.
Calculate the expected value of the random variable.
Calculate the standard deviation of this distribution.
Solutions
Expert Solution
Therefore The expectation of random variable (X) is 2.5
And standard deviation is 1.11803
orchestra answered 1 year agoRelated Solutions
Find the probability of getting 8 heads in 12 tosses of a coin.
Find the probability of getting 8 heads in 12 tosses of a
coin.
If a fair coin is tossed 25 times, the probability distribution for the number of heads,...
If a fair coin is tossed 25 times, the probability distribution
for the number of heads, X, is given below. Find the mean and the
standard deviation of the probability distribution using Excel
Enter the mean and round the standard deviation to two decimal
places.
x P(x)
0 0
1 0
2 0
3 0.0001
4 0.0004
5 0.0016
6 0.0053
7 0.0143
8 0.0322
9 0.0609
10 0.0974
11 0.1328
12 0.155
13 0.155
14 0.1328
15 0.0974
16 ...
(a) Find the exact probability of exactly 55 heads in 100 tosses of a coin. (b)...
(a) Find the exact probability of exactly 55 heads in 100 tosses
of a coin.
(b) Estimate this probability using normal distribution. Compare
your answers.
A coin is tossed with P(heads) = p. a) What is the expected number of tosses...
A coin is tossed with P(heads) = p.
a) What is the expected number of tosses required to get n
heads?
b) Determine the variance of the number of tosses needed to get
the first head.
c) Determine the variance of the number of tosses needed to get
n heads.
A coin is tossed with P(heads) = p. a) What is the expected number of tosses...
A coin is tossed with P(heads) = p.
a) What is the expected number of tosses required to get n
heads?
b) Determine the variance of the number of tosses needed to get
the first head.
c) Determine the variance of the number of tosses needed to get
n heads.
Let X be the number of heads in two tosses of a fair coin. Suppose a...
Let X be the number of heads in two tosses of a fair coin.
Suppose a fair die is rolled X+1 times after the value of X is
determined from the coin tosses. Let Y denote the total of the face
values of the X+1 rolls of the die. Find E[Y | X = x] and V[Y | X =
x] as expressions involving x. Use these conditional expected
values to find E[Y] and V[Y].
Toss a fair coin repeatedly. Let N1 be the number of tosses required to obtain heads...
Toss a fair coin repeatedly. Let N1
be the number of tosses required to obtain heads followed
immediately by tails. Let N2 be the number of tosses
required to obtain two heads in a row.
(A) Should N1 and N2
have the same expected value? If not, which expected value should
be larger? Explain your answers.
(B) Find the probability mass function of
N1.
(C) Find the expected value of N1.
(D) Find the probability mass function of
N2.
(E)...
Suppose that we are interested I the number of heads showing face up on three tosses...
Suppose that we are interested I the number of heads showing
face up on three tosses of a coin. This is the experiment. The
possible results are: zero heads, one head, two heads, and three
heads. What is the probability distribution for the number of
heads?
In a region of a country, 5% of all cell phone calls are
dropped. What is the probability that out of six randomly selected
calls, none was dropped? Exactly one? Exactly two ? exactly...
Find the probability that in 200 tosses of a fair six sided die, a five will...
Find the probability that in 200 tosses of a fair six sided die,
a five will be obtained at least 40 times
1. Amy tosses 12 biased coins. Each coin comes up heads with probability 0.2. What is...
1. Amy tosses 12 biased coins. Each coin comes up heads with
probability 0.2. What is the probability that fewer than 3 of the
coins come up heads?
Answer: 0.5583
2. Amy shoots 27000 arrows at a target. Each arrow hits the
target (independently) with probability 0.2. What is the
probability that at most 2 of the first 15 arrows hit the
target?
Answer: 0.398
3. Amy tosses 19 biased coins. Each coin comes up heads with
probability 0.1. What...
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