a) In what sense is a data set also a random variable? b) Can a data...
a) In what sense is a data set also a random variable?
b) Can a data set be a continuous random variable?
c) If f[x] is the cumulative distribution function of a continuous random variable X, how do you get the probability density function of X?
d) If f[x] is the cumulative distribution function of a discrete random variable X, what plays the role of the probability density function of X?
Homework Answers
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a) In what sense is a data set also a random variable? b) Can a data...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
PLEASE ANSWER ALL QUESTION 1 1 points Save Answer A random variable is a uniform random...
PLEASE ANSWER ALL
QUESTION 1 1 points Save Answer A random variable is a uniform random variable between 0 and 8. The probability density is 1/8, when 0<x<8 and O elsewhere. What is the probability that the random variable has a value greater than 2? QUESTION 2 1 points Save Answer The total area under a probability density curve of a continuous random variable is QUESTION 3 1 points Save Answer X is a continuous random variable with probability density...
please 6 and 7 6. (3.18, 20) A continuous random variable X that can assume values...
please 6 and 7
6. (3.18, 20) A continuous random variable X that can assume values between r = 2 and x = 5 has a density function given by f(x) = 2(1+x)/27. Find the Cumulative Distribution Function F(x). 7. (3.14) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with a cumulative distribution function x<0, F(x) = -e-41, x20 Find the probability of waiting between 3 to 7 minutes a)...
Ted value of a random variable X, denoted by E[X], is defined by two separate Definition 3.3. One...
ted value of a random variable X, denoted by E[X], is defined by two separate Definition 3.3. One formula is for discrete random variables and involves a the other formula is for continuous random variable and involves an integral. mula for handling discrete random variables, continuous random variables, and mixed discrete-continuous random variables in terms of the cumulative distributio 6 The expect function of X, that is, F(x), is F(x)dx+(1-F(x) dx. Apply this formula to (a) a discrete random variable...
Please help with this question. 12. (15 points) Let X be a continuous random variable with...
Please help with this question.
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0. F(x) = Inc. <a a<x<b bcx 1. (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F()...
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f...
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a...
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a F(x) = Inr, asi<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(x > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
7. For a discrete random variable, the set of possible values is a. an interval of...
7. For a discrete random variable, the set of possible values is a. an interval of real numbers. b. a set of numbers that is countable. c. a set of numbers that has a finite number of numbers. d. none of the above. 8. Let X be a continuous random variable, then P( X = 0) is a. 0.00001. b. zero. c. can be large in some random variable. d. none of the above. 9. For a discrete random variable,...
Give an example of a discrete or continuous random variable X (by giving the p.m.f. or...
Give an example of a discrete
or continuous random variable X (by giving the p.m.f. or p.d.f.)
whose cumulative distribution function F(x) satisfies F(n)=1-1/n!
Thank you very much!
Exercise 3.40. Give an example of a discrete or continuous random variable X p.d.f.) whose the cumulative distribution function F(x) (by giving the p.m.f satisfies F(n)1 - i for each positive integer n or
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
PLEASE ANSWER ALL
QUESTION 1 1 points Save Answer A random variable is a uniform random variable between 0 and 8. The probability density is 1/8, when 0<x<8 and O elsewhere. What is the probability that the random variable has a value greater than 2? QUESTION 2 1 points Save Answer The total area under a probability density curve of a continuous random variable is QUESTION 3 1 points Save Answer X is a continuous random variable with probability density...
please 6 and 7
6. (3.18, 20) A continuous random variable X that can assume values between r = 2 and x = 5 has a density function given by f(x) = 2(1+x)/27. Find the Cumulative Distribution Function F(x). 7. (3.14) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with a cumulative distribution function x<0, F(x) = -e-41, x20 Find the probability of waiting between 3 to 7 minutes a)...
ted value of a random variable X, denoted by E[X], is defined by two separate Definition 3.3. One formula is for discrete random variables and involves a the other formula is for continuous random variable and involves an integral. mula for handling discrete random variables, continuous random variables, and mixed discrete-continuous random variables in terms of the cumulative distributio 6 The expect function of X, that is, F(x), is F(x)dx+(1-F(x) dx. Apply this formula to (a) a discrete random variable...
Please help with this question.
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0. F(x) = Inc. <a a<x<b bcx 1. (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a F(x) = Inr, asi<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(x > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
7. For a discrete random variable, the set of possible values is a. an interval of real numbers. b. a set of numbers that is countable. c. a set of numbers that has a finite number of numbers. d. none of the above. 8. Let X be a continuous random variable, then P( X = 0) is a. 0.00001. b. zero. c. can be large in some random variable. d. none of the above. 9. For a discrete random variable,...
Give an example of a discrete
or continuous random variable X (by giving the p.m.f. or p.d.f.)
whose cumulative distribution function F(x) satisfies F(n)=1-1/n!
Thank you very much!
Exercise 3.40. Give an example of a discrete or continuous random variable X p.d.f.) whose the cumulative distribution function F(x) (by giving the p.m.f satisfies F(n)1 - i for each positive integer n or
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