Probability and Statistics: Point Estimation

Simplified binomial random variable problem: We have a binomial random variable with parameters $N$ and $\theta$. You flip a coin $n$ times with $\theta$ as the probability of heads at each toss. After flipping, you observe a numerical value $k$ for random variable $K$. Estimate $\theta$ using maximum likelihood methodology.

Independent identically distributed normal variables problem: Given $n$ independent identically distributed normal random variables with unknown mean mu and variance $v$, estimate mu and $v$ from these observations using maximum likelihood estimation.

Using Maximum Likelihood Estimation (MLE), determine the optimal mean and standard deviation for a normal distribution that best fits the measured weights of a group of mice.

We have a sample of 40 packages of rice with a mean weight of 5.7 oz and a standard deviation of 0.4 oz. Find the best estimate of the population mean.

Find the best point estimate for the mean of the population given the mean times for the 100-yard dash.

Suppose that we have a sample of data with values 5, 8, 10, 7, 10, and 14. Find the point estimate of the population mean.

Calculate the point estimate of the population standard deviation given a sample with values 5, 8, 10, 7, 10, and 14.

In a survey of 150 individuals, there are 75 responses of 'yes', 55 responses of 'no', and 20 responses of 'no opinion'. Calculate the point estimate of the proportion in the population that responded 'yes'.

In a survey of 150 individuals, there are 75 responses of 'yes', 55 responses of 'no', and 20 responses of 'no opinion'. Calculate the point estimate of the proportion in the population that responded 'no'.

Create a comprehensive estimate for a contracting job, considering factors like project scope, weather, permits, licenses, direct and indirect costs, and desired profit margin.

Suppose we want to learn about the average height in the population, which unbeknownst to us is 66 inches. If we take a sample of a few people and use their average height $\bar{x}$ to estimate $\mu$, on average, $\bar{x}$ will be equal to 66.

When estimating the variance, if the denominator in the sample variance is $n$ instead of $n-1$, and is denoted by $\cSigma^2$ instead of $s^2$, then it is a biased estimator.

Alejandro took a random sample of five ping-pong balls from a drum containing balls numbered from 0 to 32, calculated their median, replaced them, and repeated the process for 50 trials. Based on his results, does the sample median appear to be a biased or unbiased estimator of the population median?

Given dot plots for three different estimators of a population parameter with a true value of 5, determine which estimator has both low bias and low variability.