Explain how a continuous random variable can be negative.
Question:
Explain how a continuous random variable can be negative.
Random Variable:
A random variable is a function that associates a perfectly defined real number to each sample point. Sometimes the random variables are already implicit in the sample points.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerA random variable associates a real number to each value in the sample space (result set of the experiment). As a consequence, that real number can be...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Random Variable | Overview, Types & Examples
from
Chapter 5 / Lesson 1
22K
Understand what is a random variable and why it is used. Learn about the types of random variables and see examples of the random variables from everyday life.
Related to this Question
- Explain what a continuous random variable is and give some examples.
- Explain the differences between discrete random variable and continuous random variable.
- Define a continuous random variable and provide an example.
- Explain what is a dependent random variable.
- Let Y denote a continuous random variable on the interval (1, 3). What is the probability that Y will be less than 0? Explain.
- Explain how to prove something is a random variable.
- Explain how to show random variables are independent.
- Explain the differences between discrete random variables and continuous random variables.
- What is the difference between a continuous random variable and a discrete random variable?
- a. What is the difference between discrete and continuous random variables? b. Can discrete random variable be negative? c. Can continuous random variable take any value between 0 and 1?
- Explain how to show two random variables are identically distributed.
- Explain what a discrete random variable is and give some examples.
- A) Let X: non-negative, discrete, integer values random variable. Prove: B) Let X: non-negative, continuous random variable. Prove:
- Provide an example of discrete and continuous random variables.
- For any continuous random variable, the probability that the random variable takes on exactly a specific value is: a. 1.00 b. 0.50 c. any value between 0 and 1 d. 0
- Explain when to use the indicator random variable.
- Identify each of the random variables described below as discrete or continuous. a) The
- Explain why the Cauchy random variable does not have a mean.
- Give an example of a continuous probability distribution and explain why it is considered continuous.
- What is meant by a random variable?
- Define a random variable.
- Suppose X and Y are two independent continuous random variables. Please show Cov(X, Y) = 0.
- Explain why probabilities such as P(X less than x) and P(X less than or equal to x) are equal for a continuous random variable.
- Let Y be a discrete uniform random variable over {1, 2, 3}. We will define a new random variable X that is dependent on Y as we now explain. Once the experiment to obtain a realization Y=y is done. X
- Let Y be a discrete uniform random variable over {1, 2, 3} We will define a new random variable X that is dependent on Y as we now explain Once the experiment to obtain a realization Y=y is done, X wi
- Why probability of point in continuous is zero?
- Give an example of a discrete random variable.
- When rolling a die, is this an example of a discrete or continuous random variable? Explain your reasoning.
- Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. What is the probability that x will take on a value between 21 and 25?
- Let X be a random variable with a range [ 0 , ] and a continuous C D F F x ( t ) and a finite expected value. Prove that E ( X ) = 0 ( 1 F x ( t ) ) d t .
- Write the definition of two independent random variables.
- Suppose X and Y are independent continuous random variables, show that \phi(xy)= 0.
- Discuss how to check if two random variables are independent.
- What is a random variable? Give an example.
- Prove the following useful result for discrete random variable k on {0, 1, 2, . . .} E(k) = ?k P(k > k) Extend to a continuous positive random variable and apply to the exponential distribution as an example.
- Explain how to get the double expectation of two random variables.
- For a random variable, prove that: E(aX + b) = a E(X) + b.
- Determine whether the following is a continuous random variable, discrete random variable, or not a random variable. The number of statistics students now doing their homework A. It is a continuous random variable. B. It is a discrete random variable. C.
- How to find the sum of two continuous random variables?
- Let X be a continuous exponentially distributed random variable, with E[X] = 2. Let Y = 2X. What is E[Y^2]?
- Prove a random variable is a normal distribution.
- Suppose you have a random variable that is uniformly distributed between 1 and 29. What is the expected value for this random variable?
- Why is conditional expectation a random variable?
- Show that if X is a continuous random variable, then min_a E|X-a| = E|X - m|, where m is the median of X
- Why are random variables called "random"?
- a. Give an example of a random variable X such that E(X) = 8 and E(X^2) = 64. b. Explain why the answer you found in part a is the only random variable with the given values of E(X) and E(X^2). (Hint
- Explain how to calculate the third moment of the standard normal random variable.
- Let V be a continuous random variable that takes numbers from the interval [10, 15]. Find the probability of P(V=14).
- Let V be a continuous random variable that takes numbers from the interval [10, 15]. Find the probability of P(V=16).
- Show that for any random variables X and Y, E(Y |E(Y | X)) = E(Y | X).
- Select a continuous random variable (be sure to describe it), and explain whether you think it is best characterized as a uniform or normal distribution.
- Is the amount of snowfall a discrete or continuous random variable? Explain.
- a. Define the random variable x and bar x in words. b. Which distribution should be used for this problem? Explain.
- Suppose X is a continuous uniform (0,1) random variable, and define a new random variable Y=x^{(1/3)} that has the same domain (0,1). This random variable is not uniform. Find its first and second mo
- Does the central limit theorem apply to continuous random variables?
- Why is the probability that a continuous random variable is equal to a single number zero? (i.e. Why is P(X=a)=0 for any number a)
- For any continuous random variable X, if a is some real constant, then P(X = a) is always: a. dependent upon the distribution of X. b. a positive non-zero value less than or equal to 1. c. equal to a. d. equal to zero.
- Describe the difference between the probability distribution of a discrete random variable and that of a continuous random variable.
- For any continuous random variable X, if a is some real constant, then P(X = a) is always: a. a positive non-zero value less than or equal to 1. b. dependent upon the distribution of X. c. equal to a. d. equal to zero.
- A continuous random variable is a random variable that can: a. assume no continuous random frequency. b. assume any value in one or more intervals. c. have no random sample. d. assume only a countable set of values.
- Determine whether the following value is a continuous random variable, discrete random variable or not a random variable: The number of runs scored during a baseball game.
- Explain the difference between the probability distribution of a discrete random variable and that of a continuous random variable. The probability distribution of a continuous random variable possesses what two characteristics? Explain.
- A continuous random variable X has density function: f ( x ) = ? ? ? ? ? ? ? ? ? ? ? ? ? 0 f o r x < 0 2 x f o r 0 ? x ? 1 2 6 ? 6 x f o r 1 2 < x ? 1 0 f o r x > 1 Please find: (a) the mea
- Suppose a continuous random variable Y possesses the probability density function Find the value of c so that
- Let x be a continuous random variable that is normally distributed with a mean of 42 and a standard deviation of 19. Find the probability that X assumes a value less than 48.
- Let X be a continuous random variable that is normally distributed with a mean of 65 and standard deviation of 15. Find the probability that X assumes a value less than 44.
- Show that if X and Y are random variables then XeY is a random variable.
- Is the sample space the domain of a random variable? Explain.
- Fill in the blank. The two types of random variables are continuous and ________.
- Prove: If X and Y are independent random variables, then Var [X + Y ] = Var [X - Y ]
- Let V be a continuous random variable that takes numbers from the interval [10, 15]. Find the probability of P(V=10).
- Give an example of a random variable and an example of a non-random variable.
- Let X and Y be independent normal random variables with mean 0 and variance 1 . Prove that X + Y is a normal random variable with mean zero and variance 2.
- Determine whether the random variable x is discrete or continuous. Explain your reasoning. (a) Let x represent the number of books in a university library. (b) Let x represent the length of time it ta
- Suppose X is a continuous uniform (0, 1) random variable, and define a new random variable Y_1 = -3 X^2 + 4 X, that has the same domain [0, 1]. This random variable is not uniform. a. Find its cumulat
- Assume the random variable x is normally distributed with mean \mu = 83
- Determine whether the random variable x is discrete or continuous. Explain your reasoning. A) Let x represent the length (in minutes) of a movie. B) Let x represent the number of movies playing in a theater.
- If c is any constant and Y is a random variable such that E(Y) exists, show that Cov(c,Y) = 0.
- Explain why is CDF not left continuous.
- What is the difference between the probability distribution of a discrete random variable and a continuous random variable?
- Let X and Y be two independent normal random variables N(0,1). Show that X + Y and X - Y are independent random variables.
- For any continuous random variable X, if a is some real constant, then P(X a) is always the same as: a. (PX less than a) b. P(X a) c. P(X = a) d. 1 - P(X a)
- Let V be a continuous random variable that takes numbers from the interval [10, 15]. Find the probability of P(V=11).
- Suppose X and Y are continuous random variables with the joint pdf given by f(x,y)=24xy, if \ x>0.y>0,x+y<1 \\ \qquad o, \qquad otherwise Find P(Y>2X) Please explain.
- For a random variable X . a) Does there exist a value x and a random variable X , such that CDF F_x(x) greater than 1 . If yes, give an example; if not. prove it. b) Does there exist a valu
- If Y is a continuous random variable with mean mu and variance sigma^2 and if a and b are constants, prove the following. a) E(aY + b) = aE(Y ) + b = a mu + b . b) V (aY + b) = a 2V (Y ) =
- Determine whether the random variable X is discrete or continuous. Explain your thinking. a.) Let X represent the length ( in minute) of a movie. b.) Let X represent the number of movies playing in a theater.
- A continuous random variable X that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1+x)/27.
- Suppose that the random variables X and Y are independent and you know their distributions. Which of the following explains why knowing the value of X tells you nothing about the value or Y? A. The variance of X might be different from the variance of Y.
- Suppose that the random variable X has a continuous uniform distribution over (12, 30). Find P.
- Suppose that X and Y are random variables. W = COV(X,Y) is a random variable. True False
- A random variable X is a map from the sample space of an experiment to the real line R = (-infinity, infinity). Is it possible for S to be continuous and for X to be discrete? Explain and give a simple example.
- Let X be a continuous random variable with a probability density function Find the value for k.
- Explain how to get probability from a random sample.
- Suppose you have a random variable that is uniformly distributed between 44 and 71. What is the variance for this random variable? Answer to one decimal place if necessary.
- Define and explain what is meant by a probability distribution of a discrete random variable.
- Suppose that X is a discrete random variable with E(X) = 1 and E(X(X - 2)) = 3 . Find Var(-3X + 5) .
- Let X be a continuous random variable which is uniformly distributed from 1 to 8. Let U = \sqrt[3]{X} - 1. Find E(U).
- Is this an example of a discrete or continuous probability distribution? Explain.
- Continuous random variable X has a pdf f (x) = { 1 / 4, -1 less than or equal to x less than or equal to 3: 0 , otherwise. Determine the random variable Y by Y = h(X) =X^2. (a) Find E(X) and Var(X). (
Explore our homework questions and answers library
Browse
by subject