Question

Suppose X is a random variable whose probability distribution is given by the following table: X 0 2 4 6 P(X) 0.11 0.12 0.52 0.25 For each item below, write the capital letter which corresponds to the correct value. Some letters may not be used and some letters may be used more than once. • P(X is even)? • P(X < 4)? • P(X ≤ 4)? • P(X 6= 2)? • P(X = 2 and X = 6)? • P(1 < X < 3)? • Mean/Expected value of X? • Variance of X? • Standard deviation of X? A. 0.00 B. 0.12 C. 0.23 D. 0.34 E. 0.75 F. 0.88 G. 0.89 H. 1.00 I. 1.79 J. 3.28 K. Insufficient information

Answer #1

a) P(X is even) = P(X = 2) + P(X = 4) + P(X = 6) = 0.12 + 0.52 + 0.25 = 0.89

b) P(X < 4) = P(X = 0) + P(X = 2) = 0.11 + 0.12 = 0.23

c) P(X < 4) = P(X = 0) + P(X = 2) + P(X = 4) = 0.11 + 0.12 + 0.52 = 0.75

d) P(X not 2) = 1 - P(X = 2) = 1 - 0.12 = 0.88

e) P(X = 2 and X = 6) = 0

f) P(1 < X < 3) = P(X = 2) = 0.12

g) Mean = E(X) = 0 * 0.11 + 2 * 0.12 + 4 * 0.52 + 6 * 0.25 = 3.82

h) E(X^{2}) = 0^{2} * 0.11 + 2^{2} *
0.12 + 4^{2} * 0.52 + 6^{2} * 0.25 = 17.8

Variance = E(X^{2}) - (E(X))^{2} = 17.8 -
3.82^{2} = 3.2076 = 3.21

i) Standard deviation = sqrt(3.2076) = 1.79

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

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:...

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).

The random
variable x
is the number
of people who have a college degree in a randomly selected group of
four adults from a particular town. Its probability distribution is
given in the table. Find the mean
and variance of the
random
variable x.
X
0
1
2
3
4
p(x)
0.13
0.34
0.25
0.16
0.12

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.

1. Suppose a random variable X has a probability density
function
f(x)= {cx^2 -1<x<1,
{0 otherwise
where c > 0.
(a) Determine c.
(b) Find the cdf F ().
(c) Compute P (-0.5 < X < 0.75).
(d) Compute P (|X| > 0.25).
(e) Compute P (X > 0.75 | X > 0).
(f) Compute P (|X| > 0.75| |X| > 0.5).

A switchboard at some company receives calls following a
probability distribution shown below where the number of calls and
the probability of receiving those calls are recorded.
x 0 1 2 3 4 5 6 7 8 P(x) 0.04 0.05 0.15 0.02 0.28 0.03 0.20 0.11
0.12
x
0
1
2
3
4
5
6
7
8
p(x)
0.04
0.05
0.15
0.02
0.28
0.03
0.20
0.11
0.12
a. Calculate the probability that the switchboard receives:
i. Less than four calls....

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.

4) - 6) Thickets. The following discrete probability
distribution represents the number of speeding tickets in the past
12 months
X 0 1 2 3
P(X) 0.85 0.11 0.02 0.02
Compute the mean.
0.37
1.5
0.25
0.21
X 0 1 2 3
P(X) 0.85 0.11 0.02 0.02
Compute the variance
0.3249
0.57
0.3258
0.3259
X 0 1 2 3
P(X) 0.85 0.11 0.02 0.02
Compute the standard deviation.
0.5709
0.37
0.5710
0.58

In the accompanying table, the random variable x represents the
number of televisions in a household in a certain country.
Determine whether or not the table is a probability distribution.
If it is a probability distribution, find its mean and standard
deviation.
x
P(x)
0
0.02
1
0.12
2
0.34
3
0.28
4
0.14
5
0.10
If the table is a probability distribution, what is its mean?
Select the correct choice below and fill in any answer boxes within
your...

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