# Question: The state of Michigan generates a three digit number at random

The state of Michigan generates a three-digit number at random twice a day, seven days a week for its Daily 3 game. The numbers are generated one digit at a time. Consider the following set of 50 three-digit numbers as 150 one-digit integers that were generated at random:

Let X denote the outcome when a single digit is generated.

(a) With true random numbers, what is the pmf of X?

Draw the probability histogram.

(b) For the 150 observations, determine the relative frequencies of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.

(c) Draw the relative frequency histogram of the observations on the same graph paper as that of the probability histogram. Use a colored or dashed line for the relative frequency histogram.

Let X denote the outcome when a single digit is generated.

(a) With true random numbers, what is the pmf of X?

Draw the probability histogram.

(b) For the 150 observations, determine the relative frequencies of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.

(c) Draw the relative frequency histogram of the observations on the same graph paper as that of the probability histogram. Use a colored or dashed line for the relative frequency histogram.

## Answer to relevant Questions

Let a random experiment be the casting of a pair of fair dice, each having six faces, and let the random variable X denote the sum of the dice. (a) With reasonable assumptions, determine the pmf f(x) of X. (b) Draw a ...An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf Where c is a constant. Determine c and the expected value of the amount the insurance company must ...For each of the following distributions, find μ = E(X), E[X(X− 1)], and σ2 = E[X(X− 1)] + E(X) − μ2: In group testing for a certain disease, a blood sample was taken from each of n individuals and part of each sample was placed in a common pool. The latter was then tested. If the result was negative, there was no more ...The mean of a Poisson random variable X is μ = 9. Compute P(μ − 2σ < X < μ+ 2σ).Post your question