Question

The probability distribution of a random variable *X* is
given.

x |
−4 | −2 | 0 | 2 | 4 |
---|---|---|---|---|---|

=
X)x |
0.2 | 0.1 | 0.3 | 0.2 | 0.2 |

Compute the mean, variance, and standard deviation of
*X*. (Round your answers to two decimal places.)

Find mean, variance, and standard deviation

Answer #1

Solution :

x | P(x) | x * P(x) |
x^{2} * P(x) |

-4 | 0.2 | -0.8 | 3.2 |

-2 | 0.1 | -0.2 | 0.4 |

0 | 0.3 | 0 | 0 |

2 | 0.2 | 0.4 | 0.8 |

4 | 0.2 | 0.8 | 3.2 |

Sum | 1 | 0.2 | 7.6 |

Mean =
=
X * P(X) = **0.2**

Variance =
X ^{2} * P(X) -
^{2} = 7.6 - 0.2^{2} = **7.56**

Standard deviation =
= **2.75**

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X>4), n=7, p=0.4
Find the standard deviation of the following data. Round your
answer to one decimal place.
x
1
2
3
4
5
6
P(X=x)
0.1
0.1
0.2
0.1
0.2
0.3

1. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate E(X)
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
2. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate the variance of X
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
3. Given a discrete random variable, X...

The following table denotes the probability distribution for a
discrete random variable X.
x
-2
0
1
2
9
p(x)
0.1
0.3
0.2
0.3
0.1
The standard deviation of X is closest to
Group of answer choices
3.74
4.18
2.77
7.65
11

A random variable x has the following probability distribution.
Determine the standard deviation of x.
x
f(x)
0
0.05
1
0.1
2
0.3
3
0.2
4
0.35
A random variable x has the following probability distribution.
Determine the expected value of x.
x
f(x)
0
0.11
1
0.04
2
0.3
3
0.2
4
0.35
QUESTION 2
A random variable x has the following probability distribution.
Determine the variance of x.
x
f(x)
0
0.02
1
0.13
2
0.3
3
0.2...

Let x be a discrete random variable with the following
probability distribution
x: -1 , 0 , 1, 2
P(x) 0.3 , 0.2 , 0.15 , 0.35
Find the mean and the standard deviation of x

Find the mean, variance, and standard deviation of the random
variable having the probability distribution given in the following
table. (Round your answers to four decimal places.)
Random variable, x
-7
-6
-5
-4
-3
P(X = x)
0.13
0.16
0.4
0.15
0.16

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

The probability distribution of a random variable X is given
below.
x
2
4
8
9
10
P(X = x)
1⁄26
5⁄26
4⁄13
9⁄26
3⁄26
Given the mean
Find the variance (Var(X)) and the standard deviation,
respectively.

Suppose that a random variable X has the distribution (pdf) f(x)
=kx(1 -x^2) for
0 < x < 1 and zero elsewhere.
a. Find k.
b. Find P(X >0. 8)
c. Find the mean of X.
d. Find the standard deviation of X.
2. Assume that test scores for all students on a statistics test
are normally
distributed with mean 82 and standard deviation 7.
a. Find the probability that a single student scores greater than
80.
b. Find the...

Find the mean and standard deviation of the random variable X
with the following distribution:
X 0 1 2 3 4
Probability 0.1 0.2 0.3 0.3 0.1
I.
1.8, 1.29
II.
1.00, 1.00
III.
2.1, 1.135
IV.
2.1, 1.29

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