Question

Assume that the following table is the probability distribution
of X:

X 0 1 2 3

P(X) 0.10 0.30 0.40 0.20

What are the “expected value” and “standard deviation” of X? Show your work.

Answer #1

Solution:

x | P(x) | x * P(x) | x2 * P(x) |

0 | 0.1 | 0 | 0 |

1 | 0.3 | 0.3 | 0.3 |

2 | 0.4 | 0.8 | 1.6 |

3 | 0.2 | 0.6 | 1.8 |

0 | 0 | ||

Sum | 1 | 1.7 | 3.7 |

Mean = X * P(X)

= **1.7**

Standard deviation =

=X 2 * P(X) - 2

= 3.7 - (1.7)2 = 0.81

Standard deviation =
= **0.9**

xi
0 1 2 3
P(X = xi)
0.20 0.30 0.40
0.10
What is the standard deviation of X?
A
0.840
B
0.090
C
1.345
D
0.917

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x
0
1
2
P(x)
0.05
0.50
0.45
Compute the expected value of the distribution.
Consider a binomial experiment with
n = 7 trials
where the probability of success on a single trial is
p = 0.10.
(Round your answers to three decimal places.)
(a) Find
P(r = 0).
(b) Find
P(r ≥ 1)
by using the complement rule.
Compute the standard deviation of the distribution. (Round your
answer to four decimal places.)
A...

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x
0
1
2
P(x)
0.65
0.30
0.05
Compute the expected value of the distribution.
Compute the standard deviation of the distribution. (Round your
answer to four decimal places.)

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x 0 1 2
P(x) 0.05 0.20 0.75
Compute the expected value of the distribution.
Compute the standard deviation of the distribution. (Round your
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The histogram shows the distribution of stops for red traffic
lights a commuter must pass through on her way to work. Use the
histogram to find the mean, variance, standard deviation, and
expected value of the probability distribution. 0 1 2 3 4 5 0.00
0.10 0.20 0.30 0.40 x P(x) 0.03 0.25 0.35 0.14 0.14 0.09 x y graph
The mean is nothing. (Round to two decimal places as needed.)

The discrete random variable X has the following probability
distribution:
x
-10
0
5
10
p(x)
0.20
0.40
?
.10
Which one of the following correctly gives the value of the mean
and standard deviation of X? (explain/steps please)

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xi= 0, 1, 2, 3
P(X=xi)= 0.1, 0.1, 0.1, 0.7
The expected value and standard deviation is?

You are given the probability distribution below:
x
0
1
2
3
4
p(x)
0.05
0.35
0.25
0.20
0.15
Determine the standard deviation of X. Report your
answer to three decimal places.

2.
The incomplete
probability distribution table at the right is of the discrete
random variable x representing the number of times people
donate blood in 1 year. Answer the following:
x
P(X=x)
(a)
Determine the
value that is missing in the table. (Hint: what are the
requirements for a probability distribution?)
0
0.532
1
0.124
2
0.013
(b)
Find the
probability that x is at least 2 , that is find
P(x ≥ 2).
3
0.055
4
0.129
5
(c)...

Determine whether a probability distribution is given. If a
probability distribution is given, find its mean and standard
deviation. Keep fractional values to 4 significant digits.
For a small community, the probability distribution for the
number x who passed away through the last five years is as
given in the following table.
x P(x)
0 0.00
1 0.15
2 0.35
3 0.30
4 0.20
Is this a valid probability distribution?
If the mean can...

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