1. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and...

 

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1. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and 3 = 2, each of size n = 100. Compute the 500 means using the apply function and store it in x2matmn. Call this variable X₂. 2. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and 3 = 3, each of size n = 100. Compute the 500 means using the apply function and store it in x3matmn. Call this variable X3. 3. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and 3 = 4, each of size n = 100. Compute the 500 means using the apply function and store it in x4matmn. Call this variable X₁. 4. Plot the three density functions on the same graph. Add a legend so that the models can be identified. Give the plot. Interpret and compare the distributions in terms of location and spread. 5. Give the approximate distribution of X₂. (Remember a = 1.) 6. Give the approximate distribution of X3. (Remember a = 1.) 7. Give the approximate distribution of X4. (Remember a = 1.) 8. Give the approximate distribution of X₂+X3-0.5X₁. (Remember a = 1.) 1. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and 3 = 2, each of size n = 100. Compute the 500 means using the apply function and store it in x2matmn. Call this variable X₂. 2. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and 3 = 3, each of size n = 100. Compute the 500 means using the apply function and store it in x3matmn. Call this variable X3. 3. Generate a matrix containing 5000 samples from the Weibull distribution with a = 1 and 3 = 4, each of size n = 100. Compute the 500 means using the apply function and store it in x4matmn. Call this variable X₁. 4. Plot the three density functions on the same graph. Add a legend so that the models can be identified. Give the plot. Interpret and compare the distributions in terms of location and spread. 5. Give the approximate distribution of X₂. (Remember a = 1.) 6. Give the approximate distribution of X3. (Remember a = 1.) 7. Give the approximate distribution of X4. (Remember a = 1.) 8. Give the approximate distribution of X₂+X3-0.5X₁. (Remember a = 1.)