Question

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) | Find P(x ≤ 1). Describe what the resulting value represents within the given context. | 6 | 0.023 | |||||

(d) | Find the mean
μ (expected value) and standard deviation σ of
this probability distribution. |

Answer #1

a) Let the missing value be 'p'

Sum of probabilities = 1

0.532 + 0.124 + 0.013 + 0.055 + 0.129 + p + 0.023 = 1

p = 1 - 0.876

p = **0.124**

b) P(x 2) = 0.013 + 0.055 + 0.129 + 0.124 + 0.023

= **0.344**

c) P(x 1) = 0.532 + 0.124

= **0.656**

d) Mean, = 0x0.532 + 1x0.124 + 2x0.013 + 3x0.055 + 4x0.129 + 5x0.124 + 6x0.023

= **1.589**

Standard deviation, =
[(0-1.589)^{2}x0.532 + (1-1.589)^{2}x0.124 +
(2-1.589)^{2}x0.013 + (3-1.589)^{2}x0.055+
(4-1.589)^{2}x0.129 + (5-1.589)^{2}x0.124 +
(6-1.589)^{2}x0.023]^{1/2}

= **2.034**

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 >...

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

The following table lists the probability distribution of a
discrete random variable x:
x = 0,1,2,3,4,5,6,7
P(x) = 0.04, 0.11, 0.18, 0.22, 0.12, 0.21, 0.09, 0.03
a. The probability that x is less then 5:
b. The probability that x is greater then 3:
c. The probability that x is less than or equal ti 5:
d. The probability that x is greater than or equal to 4:
e. The probability that x assumes a value from 2 to 5:...

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

Determine whether or not the table is a valid probability
distribution of a discrete random variable. Explain fully.
a.
x
-2
0
2
4
P(x)
0.3
0.5
0.2
0.1
b.
x
0.5
0.25
0.25
P(x)
-0.4
0.6
0.8
c.
x
1.1
2.5
4.1
4.6
5.3
P(x)
0.16
0.14
0.11
0.27
0.22

1. Find the missing value indicated by (A) to make this a valid
discrete probability distribution.
x
-10
30
50
90
100
P(X=x)
0.05
0.10
0.25
0.15
A
2. Calculate the mean of the random variable associated with the
following discrete probability distribution. Do not round your
answer.
x
-1
0
1
P(X=x)
0.5
0.2
0.3

A random variable X has the following discrete probability
distribution.
x
12
19
22
24
27
32
p(x)
0.13
0.25
0.18
0.17
0.11
0.16
Calculate σ = standard deviation of X (up to 2 decimal places).

Determine the required value of the missing probability to make
the distribution a discrete probability distribution.
x
p(x)
3
0.32
4
?
5
0.29
6
0.12

Part II
Suppose the discrete random variable X has the
following probability distribution.
x
-2
0
2
4
6
P(X=x)
0.09
0.24
0.33
a
0.14
Find the value of a so that
this probability distribution is valid. (Sec. 4.3)
(Sec. 4.4)
Find the mean of the random variable X in Exercise 1
above.
Find the variance of the random variable X in Exercise
1 above.
Consider the following table for the number of automobiles in
Canada in 2005 by vehicle...

1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]

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