text: Functions > Statistics > Probability Distributions > Example: Probability Distributions
  Example: Probability Distributions
  Use probability distribution functions in place of probability distribution tables.
  Probability Density
  1. Use the dchisq function to calculate the probability density of a chi-squared variable, with 11 degrees of freedom, at 5.5:
  2. Use the dt function to calculate the probability density of variable t with 4 degrees of freedom, at -1.56:
  Cumulative Probability
  1. Use the pnorm function to calculate the probability that a standard normal variable exceeds 1.0:
  2. Use the pchisq function to calculate the probability that a chi-square variable, with 7 degrees of freedom, is less than 5.6:
  3. Use the pbinom function to calculate the probability that a binomial variable with size 15 and parameter 0.6 is less than or equal to 10.
  4. Use the qbinom function to calculate the probability that a binomial variable with size 15 and parameter 0.6 is less than or equal to 10.
  5. Use the rbinom function to create a vector of m=5 random numbers having the binomial distribution with size n=7 and probability of success q=0.65.
   Recalculating the worksheet causes function rbinom to return a new set of random numbers.
  6. Use the dbeta function to calculate the probability density for value x=0.8 for real shape parameters 3 and 2:
  7. Use the pbeta function to calculate the probability that a beta variable with a=3 and b=2 exceeds 0.8:
  8. Use the qbeta function to calculate the inverse cumulative probability distribution for probability p=0.8:
  9. Use the rbeta function to create a vector of m=5 random numbers having the binomial distribution with size n=6 and probability of success q=0.75.
  Inverse Cumulative Probability
  1. Use the qnorm function to calculate the inverse cumulative probability distribution for probability p:
  2. Use the qt function to calculate the inverse cumulative probability distribution for probability p:
  F-Distribution
  1. Use the dF function to calculate the 65th percentile for the F distribution with 4 and 6 degrees of freedom:
  2. Use the pF function to calculate the cumulative probability distribution for probability 0.75 with 5 and 7 degrees of freedom:
  3. Use the qF function to calculate the 95th percentile for the F distribution, with 9 and 8 degrees of freedom:
  4. Use the rF function to create a vector of 7 random numbers having the F-distribution with 2 and 3 degrees of freedom:
   Recalculating the worksheet causes function rF to return a new set of random numbers.
explanation: The document provides a series of examples and instructions for using various probability distribution functions in statistical calculations. Each example includes a specific function and parameters to calculate probabilities, densities, or generate random numbers. The document contains multiple questions or tasks, but no answers are provided.
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distilabel_metadata.content: Functions > Statistics > Probability Distributions > Example: Probability Distributions
  Example: Probability Distributions
  Use probability distribution functions in place of probability distribution tables.
  Probability Density
  1. Use the dchisq function to calculate the probability density of a chi-squared variable, with 11 degrees of freedom, at 5.5:
  2. Use the dt function to calculate the probability density of variable t with 4 degrees of freedom, at -1.56:
  Cumulative Probability
  1. Use the pnorm function to calculate the probability that a standard normal variable exceeds 1.0:
  2. Use the pchisq function to calculate the probability that a chi-square variable, with 7 degrees of freedom, is less than 5.6:
  3. Use the pbinom function to calculate the probability that a binomial variable with size 15 and parameter 0.6 is less than or equal to 10.
  4. Use the qbinom function to calculate the probability that a binomial variable with size 15 and parameter 0.6 is less than or equal to 10.
  5. Use the rbinom function to create a vector of m=5 random numbers having the binomial distribution with size n=7 and probability of success q=0.65.
   Recalculating the worksheet causes function rbinom to return a new set of random numbers.
  6. Use the dbeta function to calculate the probability density for value x=0.8 for real shape parameters 3 and 2:
  7. Use the pbeta function to calculate the probability that a beta variable with a=3 and b=2 exceeds 0.8:
  8. Use the qbeta function to calculate the inverse cumulative probability distribution for probability p=0.8:
  9. Use the rbeta function to create a vector of m=5 random numbers having the binomial distribution with size n=6 and probability of success q=0.75.
  Inverse Cumulative Probability
  1. Use the qnorm function to calculate the inverse cumulative probability distribution for probability p:
  2. Use the qt function to calculate the inverse cumulative probability distribution for probability p:
  F-Distribution
  1. Use the dF function to calculate the 65th percentile for the F distribution with 4 and 6 degrees of freedom:
  2. Use the pF function to calculate the cumulative probability distribution for probability 0.75 with 5 and 7 degrees of freedom:
  3. Use the qF function to calculate the 95th percentile for the F distribution, with 9 and 8 degrees of freedom:
  4. Use the rF function to create a vector of 7 random numbers having the F-distribution with 2 and 3 degrees of freedom:
   Recalculating the worksheet causes function rF to return a new set of random numbers.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a series of examples and instructions for using various probability distribution functions in statistical calculations. Each example includes a specific function and parameters to calculate probabilities, densities, or generate random numbers. The document contains multiple questions or tasks, but no answers are provided.
  
  Label: multiple-question