# expected value of a random variable

You randomly select a choice without even reading the questions. Consider the following PDF of a continuous random variable X. The last tab is a chance for you to try it. Expected value or Mathematical Expectation or Expectation of a random variable may be defined as the sum of products of the different values taken by the random variable and the corresponding probabilities. For only finding the center value, the Midpoint Calculator is the best option to try. In this post, I will explain the ways to answer this question. Note: The probabilities must add up to 1 because we consider all the values this random variable can take. 3.2.1 - Expected Value and Variance of a Discrete Random Variable, Lesson 1: Collecting and Summarizing Data, 1.1.5 - Principles of Experimental Design, 1.3 - Summarizing One Qualitative Variable, 1.4.1 - Minitab: Graphing One Qualitative Variable, 1.5 - Summarizing One Quantitative Variable, 3.3 - Continuous Probability Distributions, 3.3.3 - Probabilities for Normal Random Variables (Z-scores), 4.1 - Sampling Distribution of the Sample Mean, 4.2 - Sampling Distribution of the Sample Proportion, 4.2.1 - Normal Approximation to the Binomial, 4.2.2 - Sampling Distribution of the Sample Proportion, 5.2 - Estimation and Confidence Intervals, 5.3 - Inference for the Population Proportion, Lesson 6a: Hypothesis Testing for One-Sample Proportion, 6a.1 - Introduction to Hypothesis Testing, 6a.4 - Hypothesis Test for One-Sample Proportion, 6a.4.2 - More on the P-Value and Rejection Region Approach, 6a.4.3 - Steps in Conducting a Hypothesis Test for $$p$$, 6a.5 - Relating the CI to a Two-Tailed Test, 6a.6 - Minitab: One-Sample $$p$$ Hypothesis Testing, Lesson 6b: Hypothesis Testing for One-Sample Mean, 6b.1 - Steps in Conducting a Hypothesis Test for $$\mu$$, 6b.2 - Minitab: One-Sample Mean Hypothesis Test, 6b.3 - Further Considerations for Hypothesis Testing, Lesson 7: Comparing Two Population Parameters, 7.1 - Difference of Two Independent Normal Variables, 7.2 - Comparing Two Population Proportions, Lesson 8: Chi-Square Test for Independence, 8.1 - The Chi-Square Test for Independence, 8.2 - The 2x2 Table: Test of 2 Independent Proportions, 9.2.4 - Inferences about the Population Slope, 9.2.5 - Other Inferences and Considerations, 9.4.1 - Hypothesis Testing for the Population Correlation, 10.1 - Introduction to Analysis of Variance, 10.2 - A Statistical Test for One-Way ANOVA, Lesson 11: Introduction to Nonparametric Tests and Bootstrap, 11.1 - Inference for the Population Median, 12.2 - Choose the Correct Statistical Technique, Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris, Duis aute irure dolor in reprehenderit in voluptate, Excepteur sint occaecat cupidatat non proident. $$\sigma^2=\text{Var}(X)=\sum x_i^2f(x_i)-E(X)^2=\sum x_i^2f(x_i)-\mu^2$$. Find an Expected Value for a Discrete Random Variable. This has probability distribution of 1/8 for X = 0, 3/8 for X = 1, 3/8 for X = 2, 1/8 for X = 3. Let X = number of prior convictions for prisoners at a state prison at which there are 500 prisoners. You can think of an expected value as a mean, or average, for a probability distribution. Consider you take a test that has 4 multiple-choice questions. We can answer 0, 1, 2, 3, or 4 questions correctly. What would be the average value? Then sum all of those values. The probability keeps increasing as the value increases and eventually reaching the highest probability at value 8. Expected value of discrete random variables. The variance of a discrete random variable is given by: $$\sigma^2=\text{Var}(X)=\sum (x_i-\mu)^2f(x_i)$$. A discrete random variable is a random variable that can only take on a certain number of values. If you think of this PDF as a triangle-shaped uniform sheet of metal or any other material, the expected value is the x coordinate of the center of mass. Use the expected value formula to obtain: Use this table to answer the questions that follow. The expected value of a random variable is the a. most probable I value b. mean value C. most occurring value d. median value 34. Want to Be a Data Scientist? Expected Value (or mean) of a Discrete Random Variable . We know that E(X i)=µ. A Random Variable is a variable whose possible values are numerical outcomes of a random experiment. they are not equally weighted). e. Finally, which of a, b, c, and d above are complements? $$\text{Var}(X)=\left[0^2\left(\dfrac{1}{5}\right)+1^2\left(\dfrac{1}{5}\right)+2^2\left(\dfrac{1}{5}\right)+3^2\left(\dfrac{1}{5}\right)+4^2\left(\dfrac{1}{5}\right)\right]-2^2=6-4=2$$. n be independent and identically distributed random variables having distribution function F X and expected value µ. The expected value of a random variable is denoted by and it is often called the expectation of or the mean of . If this was a uniform random variable, the expected value would be 4. Formula Review. Consider the broader scope. What is the expected value for number of prior convictions?

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