Question

6. You have been provided the following probability
distribution: |
|||

Pets |
P(x) |
x*P(x) |
(x-µ)²P(x) |

0 |
0.330 |
||

1 |
0.270 |
||

2 |
0.300 |
||

3 |
0.050 |
||

4 |
0.025 |
||

5 |
0.020 |
||

6 or more |
0.005 |
||

Let x = the total number of pets in a
household |

a. Complete table |
|||

b. What is the probability of a household having no
pets? |
|||

c. What is the probability of a household having exactly 3
pets? |
|||

d. What is the probability of a household having
between 1 and 3
pets? |
|||

e. What is the probability of a household having more than
5 pets? |
|||

f. On average, how many pets does a household
have? |
|||

g. Calculate the standard deviation. |
|||

h. What is 1 standard deviations below the
mean? |
|||

i. What is 1.5 standard deviations above the
mean? |
|||

j. What is 3 standard deviations above the
mean? |

Answer #1

5.1) The joint probability distribution of the number X of cars
and the number Y of buses per signal cycle at a proposed left-turn
lane is displayed in the accompanying joint probability table.
y
p(x, y)
0
1
2
x
0
0.010
0.015
0.025
1
0.020
0.030
0.050
2
0.050
0.075
0.125
3
0.060
0.090
0.150
4
0.040
0.060
0.100
5
0.020
0.030
0.050
(a) What is the probability that there is exactly one car and
exactly one bus...

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

You are given the following Discrete Probability Distribution
p(x)
Row
x
P(x)
1
1
0.1
2
2
0.156
3
3
0.147
4
4
0.2
5
5
0.222
6
6
0.056
7
7
0.02
8
8
0.099
1
Provide the following:
Mean (Expected value)
Variance
Standard Deviation
Graph (Histogram) of the Probability Distribution

The joint probability distribution of the number X of
cars and the number Y of buses per signal cycle at a
proposed left-turn lane is displayed in the accompanying joint
probability table.
y
p(x,
y)
0
1
2
x
0
0.010
0.015
0.025
1
0.020
0.030
0.050
2
0.050
0.075
0.125
3
0.060
0.090
0.150
4
0.040
0.060
0.100
5
0.020
0.030
0.050
(a) What is the probability that there is exactly one car and
exactly one bus during...

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.
For the following distribution,
X
P(x)
0
0.130
1
0.310
2
0.350
3
0.190
4
0.020
What is the mean of the distribution?
A. 0.890
B. 1.660
C. 0.480
D. 1.042
B.
For a binomial distribution, the mean is 0.6 and n = 2. What is
π for this distribution?
A. 2.6
B. 0.3
C. 5.0
D. 1.3
C.
For a binomial distribution, the mean is 5.0 and n = 5. What is
π...

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.

Hello please Use the following discrete probability distribution
below to answer the following questions:
X p(x)
1 0.16
2 0.17
3 0.33
4 0.16
5 0.10
6 UNKNOWN
1. a What is the probability that x = 6?
P(6) = 0.08 P(6) =
0.18 P(6) =
0.24 P(6) = 0.35
1.b) What is the mean of the probability
distribution?
µ =
2.92
µ =
3.11
µ =
3.51
µ = 4.00
1.c) What is the
standard...

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).]

Let X be a normally distributed random variable with mean 5.
1. If P(4 ≤ X ≤ 4.6) = .240, find P(5.4 ≤ X ≤ 6).
2. Suppose P(X ≤ k) = .5 for some number k. What is the value of
k?
3. Suppose P(X ≤ ℓ.) = .841, for some mystery value
ℓ.. Approximately how many standard deviations above or
below the mean is the value ℓ.?

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