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![fyly)= 1- fx(²4) 1-Yy; kyco .: fyly) = {1- Yy; kyeo probability density function of y-fy Cy) =day [fy (y)] = /dy (1-²y =aldy](http://img.homeworklib.com/questions/8f5eb240-2622-11eb-a184-49453ee24570.png?x-oss-process=image/resize,w_560)
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Suppose that X is a uniform random variable on the interval...
lo (P15) Suppose X is a random variable with the uniform distribution over the interval (1.2)...
lo (P15) Suppose X is a random variable with the uniform distribution over the interval (1.2) and Y = X4 (a) Compute P[Y St] as a function of t. You need to distinguish three different cases. (b) Find the probability density function of Y and use it to compute EY).
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let...
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let t be a function. Define Y = t(X): that is, Y is the randon variable obtained by applying the function t to the value of X Transforming a random variable in this way is frequently done in statistics. In what follows, let R(X) denote the possible values of X and let R(Y) denote the possible values of To compute E[Y], we could irst find...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval...
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,...
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.
3. Let X be a continuous random variable defined on the interval 0, 4] with probability...
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?
X is a positive continuous random variable with density fX(x). Y = ln(X). Find the cumulative...
X is a positive continuous random variable with density fX(x). Y
= ln(X).
Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
Suppose that the random variables X,..Xn are i.i.d. random variables, each uniform on the interval [0,...
Suppose that the random variables X,..Xn are i.i.d. random variables, each uniform on the interval [0, 1]. Let Y1 = min(X1, ,X, and Yn = mar(X1,-..,X,H a. Show that Fri (y) = P(Ks y)-1-(1-Fri (y))". b. Show that and Fh(y) = P(, y) = (1-Fy(y))". c. Using the results from (a) and (b) and the fact that Fy (y)-y by property of uniform distribution on [0, 11, find EMI and EIYn]
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a)...
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a) Find P(X> 3). (b) Instead of following a uniform distribution, suppose that X assumes values in the interval [0, 8) according to the probability density function pictured to the right. What is h the value of h? Find P(x > 3). HINT: The area of a triangle is base x height. 2 0 0
lo (P15) Suppose X is a random variable with the uniform distribution over the interval (1.2) and Y = X4 (a) Compute P[Y St] as a function of t. You need to distinguish three different cases. (b) Find the probability density function of Y and use it to compute EY).
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let t be a function. Define Y = t(X): that is, Y is the randon variable obtained by applying the function t to the value of X Transforming a random variable in this way is frequently done in statistics. In what follows, let R(X) denote the possible values of X and let R(Y) denote the possible values of To compute E[Y], we could irst find...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
Let X be a random variable with the probability density function f(x)= x^3/4 for an interval 0<x<2 (a) What is the support of X? (b) Letting S be the support of X, pick two numbers a, b e S and compute Pa<x<b). Draw a graph that shows an area under the curve y = f() that is equal to this probability. (c) What is Fx (2)? Draw a good graph of y=Fx (I). (d) What is EX? (e) What is...
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?
X is a positive continuous random variable with density fX(x). Y
= ln(X).
Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
Suppose that the random variables X,..Xn are i.i.d. random variables, each uniform on the interval [0, 1]. Let Y1 = min(X1, ,X, and Yn = mar(X1,-..,X,H a. Show that Fri (y) = P(Ks y)-1-(1-Fri (y))". b. Show that and Fh(y) = P(, y) = (1-Fy(y))". c. Using the results from (a) and (b) and the fact that Fy (y)-y by property of uniform distribution on [0, 11, find EMI and EIYn]
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a) Find P(X> 3). (b) Instead of following a uniform distribution, suppose that X assumes values in the interval [0, 8) according to the probability density function pictured to the right. What is h the value of h? Find P(x > 3). HINT: The area of a triangle is base x height. 2 0 0
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