**Discrete Probability Distribution: Mean Calculation**Calculate the mean for the following discrete probability distribution:| $ x $ | 3 | 6 | 9 | 11 ||---------|-----|-----|-----|-----|| $ P(x) $ | 0.24 | 0.07 | 0.01 | 0.68 |**Options:**- ○ 2.178- ● 29- ○ 4.18- ○ 8.71**Explanation:**- To find the mean $ \mu $ of this distribution, use the formula: \[ \mu = \sum (x \cdot P(x)) \]- Calculation: \[ \mu = (3 \times 0.24) + (6 \times 0.07) + (9 \times 0.01) + (11 \times 0.68) \] \[ \mu = 0.72 + 0.42 + 0.09 + 7.48 = 8.71 \]- Therefore, the correct answer is 8.71.

Answered: Image /qna-images/answer/a05031e2-4821-4d12-b4c6-3de60a693e9a.jpg

Answered: Calculate the mean for the following…

Math

Statistics

Calculate the mean for the following discrete probability distribution. 6. 9. 11 P(x) 0.24 0.07 0.01 0.68

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: P(x 5. Р(х < 4) 6. Р(х < 4)

A: We have to compute the required probabilities for the random variable whose probability distribution…

Q: The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors…

Q: Calculate the mean and standard deviation of the discrete probability distribution. 0 P(x) 0.027 X 1…

A: Mean(μ)=E(X)=∑X.P(X)E(X2)=∑X2.P(X)Variance(σ2)=E(X2)-E(X)2Standard deviation(σ)=E(X2)-E(X)2

Q: 7. 2 3 P(x) 15 15 3 4 5 P(x) 25 25 25 25 9. 3 4 P(x) 10 10 20 20 10. 3 4 5 P(x) 0.212 0.113 0.125…

A: Which is the discrete probability distribution

Q: Calculate the mean for the discrete probability distribution shown here X p(x) 4.00 5.25 5.00 2 0.2…

A: Given that,x = 2,4,5,10p(x) =0.2,0.4,0.3,0.1we need to find the mean for the discrete probability…

Q: 3 4 2. 2 3 10 10 P(X) 10 10 10 2.

Q: Poisson 5. Geometric

A: Solution-: Identify the following probability distributions as discrete or continuous.

Q: Is the following a Probability Distribution Function?

A: Given : x p(x) 0 0.01 1 0.97 2 0.02 3 0.1

Q: x P(x) 0 0.25 1 0.15 2 0.3 3 0.3 Find the standard deviation of this probability distribution.…

Q: Consider the given discrete probability distribution. Find P(X>3). 1 2 3 4 5 P(x) 0.1 0.2 0.2 0.3…

Q: Find the mean of the discrete random variable X whose probability distribution is X 1 p(x) .30 2 3 4…

A: Given data is x 1 2 3 4 5 6 p(x) 0.30 0.25 0.15 0.05 0.10 0.15

Q: Determine whether the following is a probability distribution. If not, identify the requirement that…

A: Properties for discrete probability distribution:

Q: Find the missing value for P(X=2) in the probability distribution of X=no. of children ages 18 ar…

A: Solution

Q: 14. A Private bank want to know whether their mortgage rate is in line with the data history of…

A: Introduction: As the manager wishes to use a simple linear analysis to determine whether the…

Q: a) 10.99 % b) 87.19 7. CJ41.09 ). Il. Eisht pacent of all college graduates hired by companies sley…

Q: Consider the following probability distribution 1 3 4 p(x) | 0.25 | 0.5 | 0.125 | 0.125 Find a…

A: The distribution function is defined as F(x) = P(X ≤ x)

Q: x 14 15 16 17 18 P(x) 0.1 0.1 0.2 0.1 0.5 Given the discrete probability distribution above,…

A: Given information: x 14 15 16 17 18 P(x) 0.1 0.1 0.2 0.1 0.5

Q: x P(x) 0 0.15 1 0.25 2 0.1 3 0.5 Find the standard deviation of this probability distribution.…

A: x P(x) 0 0.15 1 0.25 2 0.1 3 0.5

Q: Determine whether the distribution is a discrete probability distribution. 100 200 300 400 500 D…

Q: The following table lists the income tax rates for a single person earning $50,000 per year for…

Q: Calculate the expected value for the following probability distribution: X 1 2 3 4 3.00 2.45 11.00…

A: The given probability distribution is:XP(X)10.1520.3530.440.1For the discrete random variable, Xi…

Q: ility Distribution for Number of Girls x P(x) 0.004 1 0.013 2 0.102 0.212 4 0.338 0.212 0.102 7…

A: According to guidelines we solve first three subparts only when we have given multiple subparts.

Q: Consider the joint probability distribution given below. Complete parts (a) through (c). Y Y 1 0.25…

A: The given distribution function is Y 0 1 X∨ 1 0.25 0.20 2 0.10 0.45

Q: The accompanying table describes results from groups of 10 births from 10 different sets of parents.…

A: Formula used: The maximum value in this range = μ+2σ μ = E(X) = ∑X·P(X) E(X2) = ∑X2·P(X) σ =…

Q: Calculate the mean and standard deviation of the discrete probability distribution. T 0 P(x) 0.15 5…

A: According to the given information in this question We need to find mean and standard deviation

Q: 1. Р(3) 2. Р(1) + P(4) 3. Р(х > 2)

Q: For the following probability distribution: x f(x) 0 0.01 1 0.02 2 0.10 3 0.20…

Q: 4 6. 8. P(X) 1 k 3. What should be the value of k to complete the probability distribution? A. 0 D.…

A: 3. The value of k is obtained as follows: ∑xPX=116+16+k+16+16=146+k=1k=1-46=6-46=26=13 Thus, the…

Q: The discrete random variable X has the following probability distribution: -10 0 10 p(x) 0.20 0.40…

Q: Determine the correlation for the following joint probability distribution y f(X.y) | 1/8 1 1 2 4 3…

A: Let X and Y be two random variables. Then the correlation coefficient between X and Y is given by,…

Q: Consider the following probability distribution. 1 2 3 7. P(x) 0.05 0.16 0.19 0.24 О.18 0.11 0.05…

A: According to the given information, we have The probability distribution table is given.

Q: What is the mean of the discrete random variable X with the following probability distribution?…

A: xP(x)10.2020.1030.2040.2550.25Find mean of the probability distribution.

Q: Consider the following probability distribution. 3. 4. 6 7 P(x) 0.05 0.16 0.19 0.24 0.18 0.11 0.05…

A: Given, x 0 1 2 3 4 5 6 7 P(x) 0.05 0.16 0.19 0.24 0.18 0.11 0.05 0.02

Q: (a) What is the probability that a randomly selected 49- to 52-year-old mother who had a live birth…

Q: 2. Compute the mean and variance of the following discrete probability distribution. P(x) .5 .3 10…

A: The mean of the variable X obtained as given below: Here, X denotes the observation.

Q: 2. Below is a probability distribution for the number of students with high honors. 4. 1. 0.35 P(x)…

Q: P(x) 0. 0.05 0.15 0.3 0.5 Find the standard deviation of this probability distribution. Give your…

A: Given x P(x) 0 0.05 1 0.15 2 0.3 3 0.5

Q: Given the following probability distribution, Find P(x-2) 3 4 P(x=x) 0.2 0.05 0.2 0.25 P(x-2)%=D

A: In general, the total probability is always 1.

Q: I. Which of the following are discrete probability distributions? (Yes or No) 1. 3 4 5 P(x) 0.10…

A: Property: If ∑P(X=x)=1 then it is discrete probability distribution 0≤P(X=x)≤1

Q: Which of the following is a true(legitimate) probability distribution? X PIX) -1 25 30 1 .15 10 3 25…

A: Conditions of true probability distribution: Total sum of the probabilities is equal to 1. Each…

Q: 3. 4. 0.31 P(x) 0.08 025 0.34 0.04 1. 0.03 P(x) 0.22 1.01 0.23 0.02 5. 3 0.34 4. P(x) 5. 0.06 0.05…

A: Condition for discrete probability distribution. ∑P(x)=1

Q: Find the mean and variance of the following probability distributions.

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Discrete Probability Distribution: Mean Calculation**

Calculate the mean for the following discrete probability distribution:

| $ x $ | 3 | 6 | 9 | 11 |
|---------|-----|-----|-----|-----|
| $ P(x) $ | 0.24 | 0.07 | 0.01 | 0.68 |

**Options:**

- ○ 2.178
- ● 29
- ○ 4.18
- ○ 8.71

**Explanation:**

- To find the mean $ \mu $ of this distribution, use the formula:

\[
\mu = \sum (x \cdot P(x))
\]

- Calculation:

\[
\mu = (3 \times 0.24) + (6 \times 0.07) + (9 \times 0.01) + (11 \times 0.68)
\]

\[
\mu = 0.72 + 0.42 + 0.09 + 7.48 = 8.71
\]

- Therefore, the correct answer is 8.71.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Identify the following probability distributions as discrete or continuous. Justify your answer. 20 e Geometric Poisson Source: (Google.com) Source: (Google.com)
Calculate the mean for the discrete probability distribution
Suppose the following joint probability table for X and Y. Answer the questions. X 1 3 Total -1 0.02 0.03 0.04 0.09 Y 2.75 0.03 0.15 0.16 0.34 3 0.09 0.15 0.06 0.30 4.55 0.16 0.11 0.27 Total 0.14 0.49 0.37 1.00 What is Var(Y|X = 3) – the conditional variance of Y, given that X = 3? Answer:
I. Which of the following are discrete probability distributions? (Yes or No) 1. 4 P(x) 0.10 0.20 0.25 0.40 0.05 2. 2. 3 4 5 P(x) 0.05 0.25 0.33 0.28 0,08 3. 3 4 5 P(x) 0.08 0.25 0.34 0.31 0.04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 1 2 3 4 P(x) 0,05 0.27 0.34 0,28 0.06 6. 3 4 5 P(x) 3 3 10 10 10 7. 3 4 P(x) 15 15 8. 3 4 5 P(x) 25 25 25 25 9. 3 4 P(x) 7. 1 10 10 20 20 10. 2. 3 4 5 P(x) 0.212 0.113 0,125 0.224 0.306
Identify the following probability distributions as discrete or continuous. Justify your answer. a 012 3 4 5 6 7 8 9 10 b Probability Distribution of X 0.20 0.15 0.10 0.05 0.00 2 3 45 6 7 8 9 10 11 12 Outcome 10 Fgegold
Which of the following tables represents a valid discrete probability distribution? X P(X=x) X P(X=X) X P(X=x) X P(X=x) 5 0.51 1 0.23 0 10 15 0.03 0.03 3 0.03 1 0.33 0.15 3 0.24 5 0.15 2 0.27 20 0.39 7 9 0.17 0.19 3 0.19 25 30 0.15 0.01 12 11 0.02 4 5 1.01 0.06 6 9 15 18 0.22 0.23 0.12 -0.03 0.43
II. Find the missing probability to satisfy the properties of the probability distribution. 11. 3 4 5 P(x) 0.05 0.25 0.4 0.06 12. 4 5 P(x) 0. 06 0. 23 ? 0.35 0.05 13. 3 4 5 P(x) ? 15 15 14. 5 P(x) of ? 15. X. 1 3 4. 5 P(x) 1. 10 10 4. 3. 2. 2. 2.
1. Which of the following is a probability distribution? a. x 3 6 12 15 b. x 2. 3. 5. P(x) -0.3 0.5 0.1 0.3 0.4 P(x) 1.2 1.1 1.4 1.1 1.1 C. X 2 3 4 5 d. x 1. 2. 4 5 P(x) .49 .05 32 .07 .07 P(x) -.02 0.5 0.6 0.1 1 4.
I. Which of the following are discrete probability distributions? (Yes or No) 1. 3 4 5 P(x) 0.10 0.20 0.25 0.40 0.05 2. 3 4 P(x) 0,05 0.25 0,33 0.28 0,08 3. 4 5 P(x) 0.08 0.25 0.34 0.31 0,04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 3 4 5 P(x) 0.05 0.27 0.34 0.28 0.06 6. 2 3 4 5 P(x) 1 3 3 10 10 10 7. 3. 4 P(x) 15 15 8. 2 4 5 6 P(x) 4. 25 25 25 25 9. 3 4 P(x) 1. 3. 20 20 1 10 10 10. 1 3 4 P(x) 0.212 0.113 0.125 0.224 0.306 -
is this table probability distribution compute E(x), o 1 2 3 4 P(x) 0.16 0.25 0.19 0.29 0.06
Calculate the expected value for this discrete probability distribution: X P(x) 2 0.10 3 0.25 4 0.25 5 0.40 Write you solution to two decimal places.
Which of the following is a legitimate probability distribution? (d) No. Prob 0.10 (e) No. Prob. (a) No. Prob. 1/4 (b) No. Prob. (c) No. Prob. 0.1 1. 1/4 2. 2. 0.2 2. 0.11 2. 3. 3. 3. 3. 0.25 3. -1 3 1/4 1/4 0.05 0.26 4. 4 4. 4. 0.3 4 4 1/4 04 O a Oc