Given the uniform distribution below, f(x) 0 1 2 3 4 5 6 7 8 9 10 11 12 a) What is the height of the function, f(x)? Give your answe as a reduced fraction. b) What is the probability of the shaded region? Give your answer as a reduced fraction.

Q: Suppose X has the Uniform (0, 1) distribution. Find the median of the distribution of ex correct to…

A: For a random variable (X)) that follows a uniform (0, 1) distribution, the median is the value (m))…

Q: Today, the waves are crashing onto the beach every 6 seconds. The times from when a person arrives…

A:

Q: A distribution X ~ U(2, 9). Find P(x < 6). Round answer to three decimal places.

A: We have find distribution..

Q: The population size of Batangas in 2015 is 2,600,000. This increased to 2,908,494 based on the last…

A: Since the question number is not specified, we'll be answering the first question only. Please…

Q: Suppose that X1, X2 are iid, and X1 ~ Exp(2). Find the distribution of X(1) = min{X1, X2}

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!