Question

Consider the probability distribution shown below.

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.)

Answer #1

Solution:

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

0 | 0.65 | 0 | 0 |

1 | 0.3 | 0.3 | 0.3 |

2 | 0.05 | 0.1 | 0.2 |

Sum | 1 | 0.4 | 0.5 |

Mean = X * P(X)

= **0.4**

Standard deviation =

=X 2 * P(X) - 2

= 0.5 - (0.4)2 = 0.34

Standard deviation =
= **0.5831**

Consider the probability distribution shown below.
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
answer to four decimal places.)

Consider the probability distribution shown below.
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...

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.

Consider a binomial probability distribution with p=0.65 and
n=6. Determine the probabilities below. Round to four decimal
places as needeed.
a) P(x=2)
b) P(x< or equal to1)
c) P(x>4)

Consider a random variable X with the following probability
distribution:
P(X=0) = 0.08, P(X=1) = 0.22,
P(X=2) = 0.25, P(X=3) = 0.25,
P(X=4) = 0.15, P(X=5) =
0.05
Find the expected value of X and the standard deviation of
X.

Consider the following cumulative probability
distribution.
x
0
1
2
3
4
5
P(X ≤ x)
0.10
0.29
0.48
0.68
0.84
1
a. Calculate P(X ≤ 2).
(Round your answer to 2 decimal places.)
b. Calculate P(X = 2).
(Round your answer to 2 decimal places.)
c. Calculate P(2 ≤ X ≤ 4).
(Round your answer to 2 decimal places.)

Given the following table, answer the questions below.
x
f(x)
0
0.05
1
0.2
2
0.3
3
0.45
a) Find the mean of this probability distribution. Round your
answer to one decimal place.
b) Find the standard deviation of this probability distribution.
Give your answer to at least 2 decimal places.

2.The random variable X has the probability distribution table
shown below. Calculate the standard deviation rounded to the four
decimal places.
x −1 0 4 10
P(X = x) 0.2 0.3 0.3 0.2

x
P(x)
0
0.25
1
0.05
2
0.15
3
0.55
Find the standard deviation of this probability distribution. Give
your answer to at least 2 decimal places

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.

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