Question

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*.

Answer #1

0 | 0.08 | 0 | 0 | 0 |

1 | 0.22 | 0.22 | 1 | 0.22 |

2 | 0.25 | 0.5 | 4 | 1 |

3 | 0.25 | 0.75 | 9 | 2.25 |

4 | 0.15 | 0.6 | 16 | 2.4 |

5 | 0.05 | 0.25 | 25 | 1.25 |

Let X be a random variable with the following probability
distribution: Value x of X P=Xx 1 0.15 2 0.55 3 0.05 4 0.15 5 0.10
Find the expectation EX and variance Var X of X .

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

For the probability distribution below find the mean, variance,
and standard deviation.
?
P(?)
?P (?)
?2P(?)
0
0.15
1
0.20
2
0.35
3
0.22
4
0.08
The probability distribution shows the cups of beer American
Adults consume every week. Find the expected value of cups of wine
American Adults consume every week.
?
P(?)
?P(?)
0
0.4
1
0.1
2
0.3
5
0.12
10
0.05

The following table gives the probability distribution for a
random variable X
x
P(x)
0
.028
1
.131
2
.261
3
.290
4
.194
5
.077
6
.017
7
.002
Find the mean and standard deviation
of X.

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...

x
P(X=x)
0
0.44
The incomplete
table at right is a discrete random variable x's
probability distribution, where x is the number of days in
a week people exercise. Answer the following:
1
0.18
2
0.02
3
(a)
Determine the
value that is missing in the table.
4
0.03
5
0.13
6
0.07
(b)
Explain the meaning of " P(x < 2) " as it applies to the context
of this problem.
7
0.04
(c)
Determine the
value of P(x >...

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 the following random discrete distribution.
x
x(P)
24
0.25
30
0.15
49
0.30
58
0.10
60
0.20
Calculate the mean or the expected value of X
Calculate the variance and the standard deviation of the random
variable

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)...

Problem 3. Let x be a discrete random variable with the
probability distribution given in the following table:
x = 50 100 150 200 250 300 350
p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10
(i) Find µ, σ 2 , and σ.
(ii) Construct a probability histogram for p(x).
(iii) What is the probability that x will fall in the interval
[µ − σ, µ + σ]?

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