a. If F is the cumulative distribution function of x, then what is the value of a? b. If p is the probability mass function for x, then evaluate b. c. What is the expected value of x?

Q: Let X refer to the sum of two rolled die. Describe the probabilities of each outcome. If pX(x) is…

A: It is given that x denotes the sum of two rolled dies.

Q: The probability mass function of a random variable J is given as ( J f) = { 2 where J = {-1, 0, 1} 8…

A: A probability mass function f(j) is valid if the following conditions are satisfied: 1. fj≥0∀ j2.…

Q: Consider the following table:   Value of X Probability 0 1/16 1 1/4 2 e 3 1/4 4 1/16…

A: According to the given information, for part (1) it is required to calculate the value of e. Since,…

Q: The following table gives the probability distribution for X = classes skipped yesterday by students…

A: The question is about discrete probability distribution.Given :

Q: Which of the following is/are true about continuous probability distributions? 1. The shape of the…

A: Which of the following is/are true about continuous probability distributions?

Q: A company wants to evaluate its attrition rate, in other words, how long new hires stay with the…

A: Properties of probability distribution ,  1) The sum of probabilities is 1 i.e.  ∑ P(X = xi) = 1  2)…

Q: A random experiment consists of rolling two six-sided dice A and B. A random variable, D, is defined…

A: The number of dice rolled is 2. The difference between the points of die A and Die B is  D

Q: A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a…

A: a. The probability that at least four lines are in use is, Thus, the probability that at least four…

Q: Which of the following statements are true? a. Chebychev's inequality generally requires the random…

A: Markov inequality: If X is a nonnegative random variable and a > 0, then the probability that X…

Q: Determine whether the following is a probability distribution. If not, identify the requirement that…

A: Properties for discrete probability distribution:

Q: A variable x of a finite population has the following frequency distribution: x 5 7 8 f 25 40…

A: Note:Hey there! Thank you for posting the question. However, since your question has more than 3 sub…

Q: P(x = 2) = b) What is the probability that a randomly selected person has received three tickets in…

A:

Q: Which of the following statements are true? a. Probability density functions are always less or…

A: Solution Probability density function is always non negative and less than or equal to 1.…

Q: The table below shows the results of a survey that asked 410 people whether they are involved any…

A: We have to find correct answer..

Q: Suppose that the random variable x, shown below, represents the number times. P(x) represents the…

A:

Q: What is o ? XY

A: Suppose you have the following joint probability of a stock and a bond having a positive or negative…

Q: A shuttle operator has sold 20 tickets to ride the shuttle. All passengers (ticket holder) are…

A: a. X follows a binomial distribution with parameters n=20 and p=0.65. The probability mass function…

Q: The joint probability function of random variables X and Y is given in the ta below. Show that X and…

A: y=-1 0 1 x=0 0.1 0.1 0.1 2 0.1 0.2 0.1 4 0.1 0.1 0.1 The objective is to show that X and…

Q: Consider the following cumulative probability distribution.                 x 0 1 2 3 4 5 P(X ≤ x)…

A:

Q: Suppose that the random variable z, shown below, represents the number times . P(x) represents the…

A: a) The random variable x represents the number of times a randomly selected person having received…

Q: The distribution of the time until a Web site changes is important to Web crawlers that search…

A: Calculate the probability mass function of the days until change.   The probability mass function of…

Q: A student offered random people 5 cookies total. Let X be the number of cookies that the person…

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!