Probability and Statistics Quiz
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Questions and Answers

What is the term for the set of all possible outcomes in an experiment?

  • Experiment
  • Event
  • Sample space (correct)
  • Sample point

    • Can two events with non-zero probabilities be both mutually exclusive and independent?

  • Yes, it is possible
  • No, it is not possible (correct)
  • Only if they are not dependent
  • Only if they are dependent

    • What is the term for a normal distribution with a standard deviation of 1 and a mean of 0?

  • Standard normal curve
  • Standard normal distribution (correct)
  • Probability density function
  • Normal distribution

    • In a standard normal probability distribution, what is the area to the left of the mean?

    <p>0.5</p> Signup and view all the answers

    The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the probability of a player weighing more than 241.25 pounds?

    <p>0.0495</p> Signup and view all the answers

    What type of distribution is the Poisson probability distribution?

    <p>Discrete probability distribution</p> Signup and view all the answers

    What is the range of values that the coefficient of determination can take?

    <p>Values between 0 and 1</p> Signup and view all the answers

    What is the conclusion when testing the hypothesis of slope in question 6?

    <p>Reject the null hypothesis</p> Signup and view all the answers

    What is the assumption about the variance of error in linear regression?

    <p>It is the same for all values of the independent variable</p> Signup and view all the answers

    What is the purpose of calculating the R-squared value?

    <p>To measure the goodness of fit of the model</p> Signup and view all the answers

    What is the interval estimate of the mean value of y for a given value of x?

    <p>A prediction interval</p> Signup and view all the answers

    What is the correct interpretation of a 95% confidence interval for B1?

    <p>The true value of B1 is between the interval estimates</p> Signup and view all the answers

    What is the formula for dissimilarity computation between two objects for categorical variables?

    <p>D(i, j) = p-m / p</p> Signup and view all the answers

    Which measure of deviation is more affected by an outlier in a data set?

    <p>Standard deviation</p> Signup and view all the answers

    What is the benefit of standardizing the data during clustering analysis?

    <p>It makes the variables more comparable</p> Signup and view all the answers

    Which of the following is NOT a possible termination condition in K-Means?

    <p>When all observations are assigned to a single cluster</p> Signup and view all the answers

    What is the main advantage of using mean absolute deviation over standard deviation?

    <p>It is less sensitive to outliers</p> Signup and view all the answers

    Which of the following is a possible scenario where standardization is not beneficial during clustering analysis?

    <p>When the variables have an absolute value</p> Signup and view all the answers

    What is the correct name of the library used to build a decision tree model?

    <p>DecisionTreeClassifier</p> Signup and view all the answers

    Does the Gini Index enforce the resulting tree to have multiway splits?

    <p>False</p> Signup and view all the answers

    What shape represents chance nodes in a decision tree?

    <p>Squares</p> Signup and view all the answers

    What is the measure of uncertainty of a random variable in a decision tree?

    <p>Entropy</p> Signup and view all the answers

    What is the solution to biased trees created by decision tree learners due to dominant classes?

    <p>Balance the dataset prior to fitting</p> Signup and view all the answers

    What type of tree is needed to predict the price of a house using a decision tree?

    <p>Regression Tree</p> Signup and view all the answers

    What is the number of clusters formed if a horizontal line is drawn on the y-axis for y=2?

    <p>4</p> Signup and view all the answers

    Which clustering algorithm primarily uses a merging approach?

    <p>Hierarchical</p> Signup and view all the answers

    What is the primary use of Hierarchical clustering?

    <p>Exploration</p> Signup and view all the answers

    Which metric is used to find dissimilarity between two clusters in Hierarchical clustering?

    <p>All of the above</p> Signup and view all the answers

    What is true about K-means clustering with k=3, when two variables V1 and V2 have a correlation of 1?

    <p>The cluster centroids will be in a straight line</p> Signup and view all the answers

    Which clustering algorithm works well when the shape of the clusters is hyperspherical?

    <p>K-means</p> Signup and view all the answers

    Study Notes

    Decision Trees

    • Decision tree models are built using DecisionTreeClassifier or DecisionTreeRegressor.
    • Gini Index does not enforce the resulting tree to have multiway splits.
    • Chance nodes are represented by circles.
    • Entropy is the measure of uncertainty of a random variable, characterizing the impurity of an arbitrary collection of examples.
    • End nodes are represented by squares.
    • Decision tree learners may create biased trees if some classes dominate, and the solution is to balance the dataset prior to fitting.

    Statistics

    • A standard normal distribution has a mean of 0 and a standard deviation of 1.
    • The area to the left of the mean in a standard normal probability distribution is 0.5.
    • The probability of a player weighing more than 241.25 pounds in a normal distribution with a mean of 200 pounds and a standard deviation of 25 pounds is 0.0495.
    • The probability of a player weighing less than 250 pounds in the same distribution is 0.9772.

    Probability

    • Two events having non-zero probabilities cannot be both mutually exclusive and independent.
    • A normal distribution with a standard deviation of 1 and a mean of 0 is a standard normal distribution.

    Regression Analysis

    • The coefficient of determination (R-squared) varies from 0 to 1.
    • In a regression analysis, the null hypothesis is rejected if the p-value is less than the significance level.
    • A 95% confidence interval for B1 can be calculated to test hypotheses.

    Data Analytics

    • The variance of error is not the same for all values of the independent variable.
    • The interval estimate of the mean value of y (dependent variable) for a given value of x is defined as the predicted value of y plus or minus the margin of error.
    • The formula for dissimilarity computation between two objects for categorical variables is D(i, j) = p-m / p.

    Clustering

    • Std deviation (std_f) and mean absolute deviation (s_f) are not equally affected by outliers in a dataset.
    • Standardizing the data is beneficial during clustering analysis.
    • Possible termination conditions in K-Means include a fixed number of iterations, no change in assignment of observations to clusters between iterations, and no change in centroids between successive iterations.
    • Hierarchical clustering uses a merging approach.
    • Hierarchical clustering should primarily be used for exploration.
    • Average-link is not the only metric used for finding dissimilarity between two clusters in hierarchical clustering.
    • K-means clustering is sensitive to the correlation between variables.

    CART Model

    • CART is a supervised learning technique.
    • CART adopts a greedy approach.
    • CART is suitable for building decision trees.

    Clustering Algorithms

    • K-means clustering works well when the shape of the clusters is hyperspherical.
    • Agglomerative Hierarchical clustering and Divisive Hierarchical clustering are suitable for building hierarchical clusters.

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    Description

    Test your understanding of probability and statistics concepts, including events, experiments, sample spaces, and normal distributions. Evaluate your knowledge of mutually exclusive and independent events, and standard deviations.

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