The pdf of random variable X is shown in Figure P2.10.
The numbers in parentheses indicate area. (a) Compute the value of A. (b) Compute P[2 <X< 4].
The answers should be: (a) 2.5053 (b) 0.4174
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The pdf of random variable X is shown in Figure P2.10.
The numbers in parentheses indicate...
Problem 6 he pdf of a RV X is shown in Figure 6 The numbers in...
Problem 6 he pdf of a RV X is shown in Figure 6 The numbers in parentheses indicate area. Compute the value of A fx(x) (2) ? 4 4 Figure 6pdf of a Mixed RV.
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is a...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
The PDF of random variable X and the conditionalPDF of random variable Y given X are...
The PDF of random variable X and the conditionalPDF of random variable Y given X are fX(x) = 3x2 0≤ x ≤1, 0 otherwise, fY|X(y|x) = 2y/x2 0≤ y ≤ x,0 < x ≤ 1, 0 otherwise. (1) What is the probability model for X and Y? Find fX,Y (x, y). (2) If X = 1/2, nd the conditional PDF fY|X(y|1/2). (3) If Y = 1/2, what is the conditional PDF fX|Y (x|1/2)? (4) If Y = 1/2, what is...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the rand...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
L.9) Hand calculation of expected values a) The pdf of a random variable X with the...
L.9) Hand calculation of expected values a) The pdf of a random variable X with the Exponential[u] distribution is for 0x Calculate by hand the expected value of X b) The pdf of a random variable X with the Beta[2, 3] distribution is 12 ( 1-xf x for。S$ 1. Calculate by hand the expected value of X. c) Go with numbers a and b with a<b. Calculate by hand the expected value and variance of a random variable uniformly distributed...
Let X be a random variable with PDF fx(X). Let Y be a random variable where...
Let X be a random variable with PDF fx(X). Let Y be a random variable where Y=2|X|. Find the PDF of Y, fy(y) if X is uniformly distributed in the interval [−1, 2]
For a continuous random variable X with the following probability density function (PDF): fX(x) = (...
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0...
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0 (a) What is c? Plot the pdf (b) Plot the edf of X. (c) Find P(X 0.5<0.3).
1. Let X be a random variable with variance ? > 0 and fx as a...
1. Let X be a random variable with variance ? > 0 and fx as a probability density function (pdf). The pdf is positive for all real numbers, that is fx(x) > 0. for all r ER Furthermore, the pdf fx is symmetric around zero, that is fx(x) = fx(-1), for all r ER Let y be the random variable given by Y = 4X2 +6X + with a,b,c E R. (i) For which values of a, b, and care...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = -...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
Problem 6 he pdf of a RV X is shown in Figure 6 The numbers in parentheses indicate area. Compute the value of A fx(x) (2) ? 4 4 Figure 6pdf of a Mixed RV.
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3)
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
L.9) Hand calculation of expected values a) The pdf of a random variable X with the Exponential[u] distribution is for 0x Calculate by hand the expected value of X b) The pdf of a random variable X with the Beta[2, 3] distribution is 12 ( 1-xf x for。S$ 1. Calculate by hand the expected value of X. c) Go with numbers a and b with a<b. Calculate by hand the expected value and variance of a random variable uniformly distributed...
o. Consider a random variable X with pdf given by fx(z) = 0 elsewhere. elsewhere. 0 (a) What is c? Plot the pdf (b) Plot the edf of X. (c) Find P(X 0.5<0.3).
1. Let X be a random variable with variance ? > 0 and fx as a probability density function (pdf). The pdf is positive for all real numbers, that is fx(x) > 0. for all r ER Furthermore, the pdf fx is symmetric around zero, that is fx(x) = fx(-1), for all r ER Let y be the random variable given by Y = 4X2 +6X + with a,b,c E R. (i) For which values of a, b, and care...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
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